Question: Of what form are rational primes?

Answer: 4k + 3

The fundamental theorem of arithmetic continues to hold in unique factorization domains. An example of such a domain is the Gaussian integers Z[i], that is, the set of complex numbers of the form a + bi where i denotes the imaginary unit and a and b are arbitrary integers. Its prime elements are known as Gaussian primes. Not every prime (in Z) is a Gaussian prime: in the bigger ring Z[i], 2 factors into the product of the two Gaussian primes (1 + i) and (1 − i). <hl> Rational primes (i.e. prime elements in Z) of the form 4k + 3 are Gaussian primes, whereas rational primes of the form 4k + 1 are not. <hl>

The fundamental theorem of arithmetic continues to hold in unique factorization domains. An example of such a domain is the Gaussian integers Z[i], that is, the set of complex numbers of the form a + bi where i denotes the imaginary unit and a and b are arbitrary integers. Its prime elements are known as Gaussian primes. Not every prime (in Z) is a Gaussian prime: in the bigger ring Z[i], 2 factors into the product of the two Gaussian primes (1 + i) and (1 − i). Rational primes (i.e. prime elements in Z) of the form <hl> 4k + 3 <hl> are Gaussian primes, whereas rational primes of the form 4k + 1 are not.

question: Of what form are rational primes?, context: The fundamental theorem of arithmetic continues to hold in unique factorization domains. An example of such a domain is the Gaussian integers Z[i], that is, the set of complex numbers of the form a + bi where i denotes the imaginary unit and a and b are arbitrary integers. Its prime elements are known as Gaussian primes. Not every prime (in Z) is a Gaussian prime: in the bigger ring Z[i], 2 factors into the product of the two Gaussian primes (1 + i) and (1 − i). Rational primes (i.e. prime elements in Z) of the form 4k + 3 are Gaussian primes, whereas rational primes of the form 4k + 1 are not.


Question: In what theory is the idea of a number exchanged with that of an ideal?

Answer: In ring theory

<hl> In ring theory , the notion of number is generally replaced with that of ideal. <hl> Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

<hl> In ring theory <hl>, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

<hl> In ring theory <hl> , the notion of number is generally replaced with that of ideal.

question: In what theory is the idea of a number exchanged with that of an ideal?, context: In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.


Question: What type of ideals generalize prime elements?

Answer: Prime ideals

In ring theory, the notion of number is generally replaced with that of ideal. <hl> Prime ideals , which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. <hl> The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

In ring theory, the notion of number is generally replaced with that of ideal. <hl> Prime ideals <hl>, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

<hl> Prime ideals <hl> , which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry.

question: What type of ideals generalize prime elements?, context: In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.


Question: What type of number theory utilizes and studies prime ideals?

Answer: algebraic number theory

In ring theory, the notion of number is generally replaced with that of ideal. <hl> Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. <hl> The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, <hl> algebraic number theory <hl> and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

question: What type of number theory utilizes and studies prime ideals?, context: In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.


Question: Which theorem can be simplified to the Lasker–Noether theorem?

Answer: The fundamental theorem of arithmetic

In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. <hl> The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers. <hl>

In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … <hl> The fundamental theorem of arithmetic <hl> generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

question: Which theorem can be simplified to the Lasker–Noether theorem?, context: In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.


Question: What type of commutative ring does the Lasker–Noether theorem express every ideal as an intersection of primary ideals in?

Answer: a Noetherian commutative ring

In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. <hl> The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers. <hl>

In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in <hl> a Noetherian commutative ring <hl> as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

question: What type of commutative ring does the Lasker–Noether theorem express every ideal as an intersection of primary ideals in?, context: In ring theory, the notion of number is generally replaced with that of ideal. Prime ideals, which generalize prime elements in the sense that the principal ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11), … The fundamental theorem of arithmetic generalizes to the Lasker–Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.


Question: What are the points of algebro-geometric objects?

Answer: Prime ideals

<hl> Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. <hl> Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

<hl> Prime ideals <hl> are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

question: What are the points of algebro-geometric objects?, context: Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations


Question: What does factorization of prime ideals approximate?

Answer: ramification in geometry

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. <hl> For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry . <hl> Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with <hl> ramification in geometry <hl>. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with <hl> ramification in geometry <hl> .

question: What does factorization of prime ideals approximate?, context: Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations


Question: In what type of ring can prime ideals be used for validating quadratic reciprocity?

Answer: ring of integers of quadratic number fields

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. <hl> For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations <hl>

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the <hl> ring of integers of quadratic number fields <hl> can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations

question: In what type of ring can prime ideals be used for validating quadratic reciprocity?, context: Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations


Question: What does quadratic reciprocity seek to achieve?

Answer: the solvability of quadratic equations

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. <hl> For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations <hl>

Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns <hl> the solvability of quadratic equations <hl>

question: What does quadratic reciprocity seek to achieve?, context: Prime ideals are the points of algebro-geometric objects, via the notion of the spectrum of a ring. Arithmetic geometry also benefits from this notion, and many concepts exist in both geometry and number theory. For example, factorization or ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in geometry. Such ramification questions occur even in number-theoretic questions solely concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the solvability of quadratic equations


Question: What happens to the norm when a number is multiplied by p?

Answer: norm gets smaller

<hl> In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). <hl> While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.

In particular, this <hl> norm gets smaller <hl> when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.

question: What happens to the norm when a number is multiplied by p?, context: In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.


Question: To what may general global fields be transferred to or from?

Answer: completed (or local) fields

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. <hl> Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields . <hl> This local-global principle again underlines the importance of primes to number theory.

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the <hl> completed (or local) fields <hl>. This local-global principle again underlines the importance of primes to number theory.

Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the <hl> completed (or local) fields <hl> .

question: To what may general global fields be transferred to or from?, context: In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.


Question: Completing Q with respect to what will produce the field of real numbers?

Answer: the absolute value

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). <hl> While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. <hl> These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to <hl> the absolute value <hl> yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.

question: Completing Q with respect to what will produce the field of real numbers?, context: In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.


Question: What principle highlights the significance of primes in number theory

Answer: local-global principle

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. <hl> This local-global principle again underlines the importance of primes to number theory. <hl>

In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This <hl> local-global principle <hl> again underlines the importance of primes to number theory.

question: What principle highlights the significance of primes in number theory, context: In particular, this norm gets smaller when a number is multiplied by p, in sharp contrast to the usual absolute value (also referred to as the infinite prime). While completing Q (roughly, filling the gaps) with respect to the absolute value yields the field of real numbers, completing with respect to the p-adic norm |−|p yields the field of p-adic numbers. These are essentially all possible ways to complete Q, by Ostrowski's theorem. Certain arithmetic questions related to Q or more general global fields may be transferred back and forth to the completed (or local) fields. This local-global principle again underlines the importance of primes to number theory.


Question: Which French composer wrote ametrical music using prime numbers?

Answer: Olivier Messiaen

Prime numbers have influenced many artists and writers. <hl> The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". <hl> In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

Prime numbers have influenced many artists and writers. The French composer <hl> Olivier Messiaen <hl> used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

question: Which French composer wrote ametrical music using prime numbers?, context: Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".


Question: What is one work by Olivier Messiaen?

Answer: La Nativité du Seigneur

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". <hl> In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". <hl> According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as <hl> La Nativité du Seigneur <hl> (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

question: What is one work by Olivier Messiaen?, context: Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".


Question: What is another piece created by Olivier Messiaen?

Answer: Quatre études de rythme

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". <hl> In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". <hl> According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and <hl> Quatre études de rythme <hl> (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

question: What is another piece created by Olivier Messiaen?, context: Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".


Question: In which etude of Neumes rythmiques do the primes 41, 43, 47 and 53 appear in?

Answer: the third étude

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". <hl> In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude , "Neumes rythmiques". <hl> According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in <hl> the third étude <hl>, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".

In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in <hl> the third étude <hl> , "Neumes rythmiques".

question: In which etude of Neumes rythmiques do the primes 41, 43, 47 and 53 appear in?, context: Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".


Question: Messiaen says that composition with prime numbers was inspired by what?

Answer: the movements of nature

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". <hl> According to Messiaen this way of composing was "inspired by the movements of nature , movements of free and unequal durations". <hl>

Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by <hl> the movements of nature <hl>, movements of free and unequal durations".

According to Messiaen this way of composing was "inspired by <hl> the movements of nature <hl> , movements of free and unequal durations".

question: Messiaen says that composition with prime numbers was inspired by what?, context: Prime numbers have influenced many artists and writers. The French composer Olivier Messiaen used prime numbers to create ametrical music through "natural phenomena". In works such as La Nativité du Seigneur (1935) and Quatre études de rythme (1949–50), he simultaneously employs motifs with lengths given by different prime numbers to create unpredictable rhythms: the primes 41, 43, 47 and 53 appear in the third étude, "Neumes rythmiques". According to Messiaen this way of composing was "inspired by the movements of nature, movements of free and unequal durations".


Question: Where does the Rhine begin?

Answer: Swiss canton

<hl> The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. <hl> The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the <hl> Swiss canton <hl> of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: Where does the Rhine begin?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: Where does the Rhine empty?

Answer: North Sea

<hl> The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. <hl> The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the <hl> North Sea <hl> in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: Where does the Rhine empty?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: What is the largest city the Rhine runs through?

Answer: Cologne, Germany

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. <hl> The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. <hl> It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is <hl> Cologne, Germany <hl> with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: What is the largest city the Rhine runs through?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: What river is larger than the Rhine?

Answer: Danube

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. <hl> It is the second-longest river in Central and Western Europe (after the Danube ), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s). <hl>

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the <hl> Danube <hl>), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

It is the second-longest river in Central and Western Europe (after the <hl> Danube <hl> ), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: What river is larger than the Rhine?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: How long is the Rhine?

Answer: 1,230 km (760 mi)

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. <hl> It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi) ,[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s). <hl>

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about <hl> 1,230 km (760 mi) <hl>,[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

It is the second-longest river in Central and Western Europe (after the Danube), at about <hl> 1,230 km (760 mi) <hl> ,[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: How long is the Rhine?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: Where is the Rhine?

Answer: Europe

<hl> The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a Europe an river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. <hl> The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a <hl> Europe <hl>an river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a <hl> Europe <hl> an river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands.

question: Where is the Rhine?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: What country does the Rhine empty?

Answer: Netherlands

<hl> The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands . <hl> The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the <hl> Netherlands <hl>. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the <hl> Netherlands <hl> .

question: What country does the Rhine empty?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: How long is the Rhine?

Answer: 1,230 km

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. <hl> It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s). <hl>

The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about <hl> 1,230 km <hl> (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).

question: How long is the Rhine?, context: The Rhine (Romansh: Rein, German: Rhein, French: le Rhin, Dutch: Rijn) is a European river that begins in the Swiss canton of Graubünden in the southeastern Swiss Alps, forms part of the Swiss-Austrian, Swiss-Liechtenstein border, Swiss-German and then the Franco-German border, then flows through the Rhineland and eventually empties into the North Sea in the Netherlands. The biggest city on the river Rhine is Cologne, Germany with a population of more than 1,050,000 people. It is the second-longest river in Central and Western Europe (after the Danube), at about 1,230 km (760 mi),[note 2][note 1] with an average discharge of about 2,900 m3/s (100,000 cu ft/s).


Question: Where does the name Rhine derive from?

Answer: Gaulish name Rēnos

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos , which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the <hl> Gaulish name Rēnos <hl>, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the <hl> Gaulish name Rēnos <hl> , which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: Where does the name Rhine derive from?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the French name for the Rhine?

Answer: Rhin

<hl> The variant forms of the name of the Rhin e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the <hl> Rhin <hl>e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the <hl> Rhin <hl> e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What is the French name for the Rhine?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the Proto-Germanic adaptation of the name of the Rhine?

Answer: Rīnaz

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as * Rīnaz , via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *<hl> Rīnaz <hl>, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as * <hl> Rīnaz <hl> , via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What is the Proto-Germanic adaptation of the name of the Rhine?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What century did the name of the Rhine come from?

Answer: 1st century BC

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography ( 1st century BC ) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (<hl> 1st century BC <hl>) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography ( <hl> 1st century BC <hl> ) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What century did the name of the Rhine come from?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What does the name The Rhine come from?

Answer: Gaulish name Rēnos

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos , which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the <hl> Gaulish name Rēnos <hl>, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the <hl> Gaulish name Rēnos <hl> , which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What does the name The Rhine come from?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the Rhine called in French?

Answer: Rhin

<hl> The variant forms of the name of the Rhin e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the <hl> Rhin <hl>e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the <hl> Rhin <hl> e in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What is the Rhine called in French?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the Rhine called in Dutch?

Answer: Rijn

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch <hl> Rijn <hl> (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

question: What is the Rhine called in Dutch?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the Proto-Germanic adoption of the Gaulish name of the Rhine?

Answer: Rīnaz

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as * Rīnaz , via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *<hl> Rīnaz <hl>, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as * <hl> Rīnaz <hl> , via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)).

question: What is the Proto-Germanic adoption of the Gaulish name of the Rhine?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: How was the Dutch name for the Rhine originally spelled?

Answer: Rhijn

<hl> The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn )). <hl> The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled <hl> Rhijn <hl>)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.

The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled <hl> Rhijn <hl> )).

question: How was the Dutch name for the Rhine originally spelled?, context: The variant forms of the name of the Rhine in modern languages are all derived from the Gaulish name Rēnos, which was adapted in Roman-era geography (1st century BC) as Greek Ῥῆνος (Rhēnos), Latin Rhenus.[note 3] The spelling with Rh- in English Rhine as well as in German Rhein and French Rhin is due to the influence of Greek orthography, while the vocalisation -i- is due to the Proto-Germanic adoption of the Gaulish name as *Rīnaz, via Old Frankish giving Old English Rín, Old High German Rīn, Dutch Rijn (formerly also spelled Rhijn)). The diphthong in modern German Rhein (also adopted in Romansh Rein, Rain) is a Central German development of the early modern period, the Alemannic name Rī(n) retaining the older vocalism,[note 4] as does Ripuarian Rhing, while Palatine has diphthongized Rhei, Rhoi. Spanish is with French in adopting the Germanic vocalism Rin-, while Italian, Occitan and Portuguese retain the Latin Ren-.


Question: What is the conventional method to measure the Rhine?

Answer: Rhine-kilometers

<hl> The length of the Rhine is conventionally measured in " Rhine-kilometers " (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). <hl> The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

The length of the Rhine is conventionally measured in "<hl> Rhine-kilometers <hl>" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

The length of the Rhine is conventionally measured in " <hl> Rhine-kilometers <hl> " (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km).

question: What is the conventional method to measure the Rhine?, context: The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]


Question: When was the scale to measure the Rhine introduced?

Answer: 1939

<hl> The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). <hl> The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in <hl> 1939 <hl> which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

question: When was the scale to measure the Rhine introduced?, context: The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]


Question: Where does the Rhine river's measurement begin?

Answer: Old Rhine Bridge at Constance

<hl> The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). <hl> The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the <hl> Old Rhine Bridge at Constance <hl> (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

question: Where does the Rhine river's measurement begin?, context: The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]


Question: Where does the Rhine river's measurement end?

Answer: Hoek van Holland

<hl> The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). <hl> The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to <hl> Hoek van Holland <hl> (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]

question: Where does the Rhine river's measurement end?, context: The length of the Rhine is conventionally measured in "Rhine-kilometers" (Rheinkilometer), a scale introduced in 1939 which runs from the Old Rhine Bridge at Constance (0 km) to Hoek van Holland (1036.20 km). The river length is significantly shortened from the river's natural course due to number of canalisation projects completed in the 19th and 20th century.[note 7] The "total length of the Rhine", to the inclusion of Lake Constance and the Alpine Rhine is more difficult to measure objectively; it was cited as 1,232 kilometres (766 miles) by the Dutch Rijkswaterstaat in 2010.[note 1]