Greek Geometry - Euclid, Pythagoras, Archimedes and Thales Greek Geometry Greek Geometry - Euclid, Pythagoras, Archimedes and Thales . This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: 8.6Mental Hospitals Save this course for later Don't have time for it all now? No problem, save it as a course and come back to it later. Like Explorable? Take it with you wherever you go. Download Explorable Now! Subscribe to our RSS Feed Like us on Facebook Share this page on your website: <a href="">Greek Geometry</a> Geometry can conceivably lay claim to being the oldest branch of mathematics outside arithmetic, and humanity has probably used geometrical techniques since before the dawn of recorded history. Initially, as with the Egyptians, geometry originated from practical necessity and the need to measure land; the word 'Geometry' means 'Earth Measuring'. This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: .

Euclid, illustrating geometry in "The School of Athens", by Raffaello Sanzio (Public Domain) Certainly, for measuring boundaries and for erecting buildings, humans need to have some inbuilt mechanism and instinct for judging distances, angles, and height. As civilizations developed, these instincts were augmented by observations and procedures gained from experience, experimentation, and intuition. The Babylonians were certainly skilled geometers, and the Egyptians developed a rich and complex mathematics based around surveying. Both of these cultures would pass their information on to the Greeks. . The Start of Greek Geometry The Egyptians and the Babylonians were not really interested in finding out axioms and underlying principles governing geometry. Their approach was very pragmatic and aimed very much at practical uses. The Babylonians, for example, assumed that Pi was exactly 3, and saw no reason to change this. The Egyptian mathematicians had no structure to their geometry, just a collection of rules and solutions aimed at specific circumstances, such as calculating the volume of a truncated pyramid. They also used trigonometry at that point, in development of a subset of geometry, for surveying and for measuring the dimensions of pyramids. These cultures did not appear to use deductive reasoning to uncover geometric techniques from first principles.

Instead, they used trial and error and, if a solution was not readily available, used trial and error to arrive at an approximation. However, these cultures laid the foundations of Greek geometry and influenced the Greeks, who would bring a deductive methodology to geometry, trying to find elegant rules underpinning the field. . Early Greek Geometry Thales of Miletus (Public Domain) The early history of Greek geometry is unclear, because no original sources of information remain and all of our knowledge is from secondary sources written many years after the early period. However, we can still see a decent overview and also start to look at some of the great names, the Greek mathematicians who would shape the course of Greek geometry. The first, and one of the greatest names, is Thales of Miletus, a mathematician living in the 6th century BCE. He is regarded as the father of geometry and began the process of using deduction from first principles. It is believed that he travelled to Egypt and Babylon, picking up geometric techniques from these cultures, and he certainly would have had access to their work. Thales strongly believed that reasoning should supersede experimentation and intuition, and began to look for solid principles upon which he could build theorems.

This introduced the idea of proof into geometry and he proposed some axioms that he believed to be mathematical truths. A circle is bisected by any of its diameters The base angles of an isosceles triangle are equal When two straight lines cross, the opposing angles are equal An angle drawn in a semi-circle is a right angle Two triangles with one equal side and two equal angles are congruent Thales is credited with devising a method for finding the height of a ship at sea, a technique that he used to measure the height of a pyramid, much to the delight of the Egyptians. For this, he had to understand proportion and possibly the rules governing similar triangles, one of the staples of trigonometry and geometry. It is unclear exactly how Thales decided that the above axioms were irrefutable proofs, but they were incorporated into the body of Greek mathematics and the influence of Thales would influence countless generations of mathematicians. Pythagoras Pythagoras (Public Domain) Probably the most famous name during the development of Greek geometry is Pythagoras , even if only for the famous law concerning right angled triangles. This mathematician lived in a secret society which took on a semi-religious mission.

From this, the Pythagoreans developed a number of ideas and began to develop trigonometry. The Pythagoreans added a few new axioms to the store of geometrical knowledge. The sum of the internal angles of a triangle equals two right angles *(180o). The sum of the external angles of a triangle equals four right angles (360o). The sum of the interior angles of any polygon equals 2n-4 right angles, where n is the number of sides. The sum of the exterior angles of a polygon equals four right angles, however many sides. The three polygons, the triangle, hexagon, and square completely fill the space around a point on a plane - six triangles, four squares and three hexagons. In other words, you can tile an area with these three shapes, without leaving gaps or having overlaps. For a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Most of these rules are instantly familiar to most students, as basic principles of geometry and trigonometry. One of his pupils, Hippocrates , took the development of geometry further.

He was the first to start using geometrical techniques in other areas of maths, such as solving quadratic equations, and he even began to study the process of integration. He studied the problem of Squaring the Circle (which we now know to be impossible, simply because Pi is an irrational number). He solved the problem of Squaring a Lune and showed that the ratio of the areas of two circles equalled the ratio between the squares of the radii of the circles. Euclid Euclid meant that all mathematical statements should be proved ( Euclid's Elements ) Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He gathered the work of all of the earlier mathematicians and created his landmark work, 'The Elements,' surely one of the most published books of all time. In this work, Euclid set out the approach for geometry and pure mathematics generally, proposing that all mathematical statements should be proved through reasoning and that no empirical measurements were needed. This idea of proof still dominates pure mathematics in the modern world. Archimedes Archimedes was a great mathematician and was a master at visualising and manipulating space.

He perfected the methods of integration and devised formulae to calculate the areas of many shapes and the volumes of many solids. He often used the method of exhaustion to uncover formulae. For example, he found a way to mathematically calculate the area underneath a parabolic curve; calculated a value for Pi more accurately than any previous mathematician; and proved that the area of a circle is equal to Pi multiplied by the square of its radius. He also showed that the volume of a sphere is two thirds the volume of a cylinder with the same height and radius. This last discovery was engraved into his tombstone. Apollonius of Perga (262 - 190 BCE) Appolonius of Pergia (Public Domain) Apollonius was a mathematician and astronomer, and he wrote a treatise called 'Conic Sections.' Apollonius is credited with inventing the words ellipse, parabola, and hyperbola, and is often referred to as the Great Geometer. He also wrote extensively on the ideas of tangents to curves, and his work on conics and parabolas would influence the later Islamic scholars and their work on optics. .

Greek Geometry and Its Influence Greek geometry eventually passed into the hands of the great Islamic scholars, who translated it and added to it. In this study of Greek geometry, there were many more Greek mathematicians and geometers who contributed to the history of geometry, but these names are the true giants, the ones that developed geometry as we know it today. . Euclid: Biography & Father Of Geometry | Online Homework Help | SchoolWorkHelper Euclid: Biography & Father Of Geometry You are here: PDF Very little is known of the father of geometry, also known as Euclid. Records show that he lived somewhere around 300 B.C., but that date is sketchy. He was a Greek mathematician and is probably best known for his work Elements. Since little is known about the personal life of Euclid, it is difficult to do a biography on him. His chief work, entitled Elements, is a comprehensive treatise on mathematics.

It includes 13 volumes that entail such subjects as plane geometry, dealing with the properties of flat surfaces and of planar figures, such as the triangle; proportion in general, a particular kind of relation between groups of numbers or quantities; the properties of numbers; incommensurable magnitudes; and solid geometry, branch of geometry that deals with the properties and measurement of geometric figures in three-dimensional space. Some people say that the geometrical sections of Elements were actually rearrangements of Exodus previous work. However Euclid himself is said to have made several discoveries in his Number Theory, which is a branch of mathematics that deals with the properties and relationships of numbers. Most historians believe Euclid was educated at Athens. His teachers may have included pupils of Plato, who was a philosopher and one of the most influential thinkers in Western philosophy. Euclid tought geometry in Alexandria and opened a school of mathematics there. He also wrote Data, which was a collection of geometrical theorems; Phenomena, a description of the heavens; and The Division of the Scale, which is a mathematical discussion of music.

But yet again many historians believe many of these works (other than the Elements) were spuriously credited to him, others disagree and say that indeed his works are that of his own. Euclid’s Elements was used as a text for 2000 years, and even today a modified version of its first few books forms the basis of high school instruction in plane geometry. The first printed edition of Euclid’s works was a translation from Arabic to Latin, which appeared at Venice in 1482. Euclid is called the father of geometry. He has earned the respect from all mathematicians, and is regarded as the creator of the Elements, which is based on almost every point of geometry. Students learn about him every time they open their math book Related posts: Euclid | Greek mathematician | Britannica.com Greek mathematician Euclid, Greek Eukleides (born c. 300 bce, Alexandria, Egypt), the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry , the Elements. Life Of Euclid’s life nothing is known except what the Greek philosopher Proclus (c.

410–485 ce) reports in his “summary” of famous Greek mathematicians. According to him, Euclid taught at Alexandria in the time of Ptolemy I Soter , who reigned over Egypt from 323 to 285 bce. Medieval translators and editors often confused him with the philosopher Eukleides of Megara , a contemporary of Plato about a century before, and therefore called him Megarensis. Proclus supported his date for Euclid by writing “Ptolemy once asked Euclid if there was not a shorter road to geometry than through the Elements, and Euclid replied that there was no royal road to geometry.” Today few historians challenge the consensus that Euclid was older than Archimedes (c. 290–212/211 bce). Sources and contents of the Elements Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 bce), not to be confused with the physician Hippocrates of Cos (c. 460–375 bce).

The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384–322 bce). The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids . A brief survey of the Elements belies a common belief that it concerns only geometry . This misconception may be caused by reading no further than Books I through IV, which cover elementary plane geometry. Euclid understood that building a logical and rigorous geometry (and mathematics ) depends on the foundation—a foundation that Euclid began in Book I with 23 definitions (such as “a point is that which has no part” and “a line is a length without breadth”), five unproved assumptions that Euclid called postulates (now known as axioms ), and five further unproved assumptions that he called common notions. Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem .

(For Euclid’s proof of the theorem, see Sidebar: Euclid’s Windmill Proof .) Euclid’s axioms Things that coincide with one another are equal. 10 The whole is greater than a part. The subject of Book II has been called geometric algebra because it states algebraic identities as theorems about equivalent geometric figures. Book II contains a construction of “the section,” the division of a line into two parts such that the ratio of the larger to the smaller segment is equal to the ratio of the original line to the larger segment. (This division was renamed the golden section in the Renaissance after artists and architects rediscovered its pleasing proportions.) Book II also generalizes the Pythagorean theorem to arbitrary triangles, a result that is equivalent to the law of cosines (see plane trigonometry ). Book III deals with properties of circles and Book IV with the construction of regular polygons, in particular the pentagon. Britannica Stories Ringling Bros. Folds Its Tent Book V shifts from plane geometry to expound a general theory of ratios and proportions that is attributed by Proclus (along with Book XII) to Eudoxus of Cnidus (c.

395/390–342/337 bce). While Book V can be read independently of the rest of the Elements, its solution to the problem of incommensurables ( irrational numbers ) is essential to later books. In addition, it formed the foundation for a geometric theory of numbers until an analytic theory developed in the late 19th century. Book VI applies this theory of ratios to plane geometry, mainly triangles and parallelograms, culminating in the “application of areas,” a procedure for solving quadratic problems by geometric means. Mathematics Books VII–IX contain elements of number theory , where number (arithmos) means positive integers greater than 1. Beginning with 22 new definitions—such as unity, even, odd, and prime —these books develop various properties of the positive integers. For instance, Book VII describes a method, antanaresis (now known as the Euclidean algorithm ), for finding the greatest common divisor of two or more numbers; Book VIII examines numbers in continued proportions, now known as geometric sequences (such as ax, ax2, ax3, ax4…); and Book IX proves that there are an infinite number of primes.

According to Proclus, Books X and XIII incorporate the work of the Pythagorean Theaetetus (c. 417–369 bce). Book X, which comprises roughly one-fourth of the Elements, seems disproportionate to the importance of its classification of incommensurable lines and areas (although study of this book would inspire Johannes Kepler [1571–1630] in his search for a cosmological model). Britannica Lists & Quizzes Editor Picks: Exploring 10 Types of Basketball Movies Books XI–XIII examine three-dimensional figures, in Greek stereometria. Book XI concerns the intersections of planes, lines, and parallelepipeds (solids with parallel parallelograms as opposite faces). Book XII applies Eudoxus’s method of exhaustion to prove that the areas of circles are to one another as the squares of their diameters and that the volumes of spheres are to one another as the cubes of their diameters. Book XIII culminates with the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) in a given sphere, as displayed in the animation .

The unevenness of the several books and the varied mathematical levels may give the impression that Euclid was but an editor of treatises written by other mathematicians. To some extent this is certainly true, although it is probably impossible to figure out which parts are his own and which were adaptations from his predecessors. Euclid’s contemporaries considered his work final and authoritative; if more was to be said, it had to be as commentaries to the Elements. Renditions of the Elements In ancient times, commentaries were written by Heron of Alexandria (flourished 62 ce), Pappus of Alexandria (flourished c. 320 ce), Proclus, and Simplicius of Cilicia (flourished c. 530 ce). The father of Hypatia , Theon of Alexandria (c. 335–405 ce), edited the Elements with textual changes and some additions; his version quickly drove other editions out of existence, and it remained the Greek source for all subsequent Arabic and Latin translations until 1808, when an earlier edition was discovered in the Vatican.

The immense impact of the Elements on Islamic mathematics is visible through the many translations into Arabic from the 9th century forward, three of which must be mentioned: two by al-Ḥajjāj ibn Yūsuf ibn Maṭar, first for the ʿAbbāsid caliph Hārūn al-Rashīd (ruled 786–809) and again for the caliph al-Maʾmūn (ruled 813–833); and a third by Isḥāq ibn Ḥunayn (died 910), son of Ḥunayn ibn Isḥāq (808–873), which was revised by Thābit ibn Qurrah (c. 836–901) and again by Naṣīr al-Dīn al-Ṭūsī (1201–74). Euclid first became known in Europe through Latin translations of these versions.

Connect with Britannica Facebook Twitter YouTube Instagram Pinterest The first extant Latin translation of the Elements was made about 1120 by Adelard of Bath , who obtained a copy of an Arabic version in Spain, where he traveled while disguised as a Muslim student. Adelard also composed an abridged version and an edition with commentary, thus starting a Euclidean tradition of the greatest importance until the Renaissance unearthed Greek manuscripts. Incontestably the best Latin translation from Arabic was made by Gerard of Cremona (c. 1114–87) from the Isḥāq-Thābit versions. The first direct translation from the Greek without an Arabic intermediary was made by Bartolomeo Zamberti and published in Vienna in Latin in 1505, and the editio princeps of the Greek text was published in Basel in 1533 by Simon Grynaeus. The first English translation of the Elements was by Sir Henry Billingsley in 1570.

The impact of this activity on European mathematics cannot be exaggerated; the ideas and methods of Kepler , Pierre de Fermat (1601–65), René Descartes (1596–1650), and Isaac Newton (1642 [Old Style]–1727) were deeply rooted in, and inconceivable without, Euclid’s Elements. Other writings The Euclidean corpus falls into two groups: elementary geometry and general mathematics. Although many of Euclid’s writings were translated into Arabic in medieval times, works from both groups have vanished. Extant in the first group is the Data (from the first Greek word in the book, dedomena [“given”]), a disparate collection of 94 advanced geometric propositions that all take the following form: given some item or property, then other items or properties are also “given”—that is, they can be determined. Some of the propositions can be viewed as geometry exercises to determine if a figure is constructible by Euclidean means.

On Divisions (of figures)—restored and edited in 1915 from extant Arabic and Latin versions—deals with problems of dividing a given figure by one or more straight lines into various ratios to one another or to other given areas. Four lost works in geometry are described in Greek sources and attributed to Euclid. The purpose of the Pseudaria (“Fallacies”), says Proclus, was to distinguish and to warn beginners against different types of fallacies to which they might be susceptible in geometrical reasoning. According to Pappus, the Porisms (“Corollaries”), in three books, contained 171 propositions. Michel Chasles (1793–1880) conjectured that the work contained propositions belonging to the modern theory of transversals and to projective geometry . Like the fate of earlier “Elements,” Euclid’s Conics, in four books, was supplanted by a more thorough book on the conic sections with the same title written by Apollonius of Perga (c. 262–190 bce). Pappus also mentioned the Surface-loci (in two books), whose subject can only be inferred from the title.

Trending Topics Eyjafjallajökull volcano Among Euclid’s extant works are the Optics , the first Greek treatise on perspective, and the Phaenomena, an introduction to mathematical astronomy. Those works are part of a corpus known as “the Little Astronomy” that also includes the Moving Sphere by Autolycus of Pitane. Two treatises on music, the “Division of the Scale” (a basically Pythagorean theory of music ) and the “Introduction to Harmony,” were once mistakenly thought to be from The Elements of Music, a lost work attributed by Proclus to Euclid. Assessment Almost from the time of its writing, the Elements exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, other than the Bible , the Elements is the most translated, published, and studied of all the books produced in the Western world.

Euclid may not have been a first-class mathematician, but he set a standard for deductive reasoning and geometric instruction that persisted, practically unchanged, for more than 2,000 years. Euclid - Student Encyclopedia (Ages 11 and up) It has been said that, next to the Bible, the Elements of Euclid is the most-translated, -published, and -studied book in the Western world. Of the author himself almost nothing is known. It is recorded that he founded and taught at a school of mathematics in Alexandria, Egypt, during the reign of Ptolemy I Soter, who ruled from 323 to about 283 BC. It is assumed from his books that he was not a first-class mathematician, but he was a first-rate teacher of geometry and arithmetic. The Elements remained unchallenged for more than 2,000 years. Not until the mid-19th century was a non-Euclidean geometry devised.

Article Contributors Euclid, the Father of Geometry - Greek Mathematics Euclid, the Father of Geometry Greek Mathematics Share this page on your website: <a href="">Euclid, the Father of Geometry</a> Greek Mathematics Euclid enters history as one of the greatest of all mathematicians and he is often referred to as the father of geometry. The standard geometry most of us learned in school is called Euclidian Geometry. This article is a part of the guide: Select from one of the other courses available: Discover 44 more articles on this topic Don't miss these related articles: . Statue of Euclid in Oxford (Public Domain) Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called 'The Elements' (c300 BCE). This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. Euclid probably attended Plato's academy in Athens before moving to Alexandria, in Egypt. At this time, the city had a huge library and the ready availability of papyrus made it the center for books, the major reasons why great minds such as Heron of Alexandria and Euclid based themselves there.

. Euclid's Elements Euclid's Elements Title Page (Public Domain) Euclid's great work consisted of thirteen books covering a vast body of mathematical knowledge, spanning arithmetic, geometry and number theory. The books are organized by subjects, covering every area of mathematics developed by the Greeks: Books I - IV, and Book VI: Plane Geometry Books XI - XIII: Solid Geometry Books V and X: Magnitudes and Ratios Books VII - IX: Whole Numbers The basic structure of the elements begins with Euclid establishing axioms, the starting point from which he developed 465 propositions, progressing from his first established principles to the unknown in a series of steps, a process that he called the 'Synthetic Approach.' He looked at mathematics as a whole, but was concentrated on geometry and that particular discipline formed the basis of his work. . . Euclid's Axioms Euclid based his approach upon 10 axioms, statements that could be accepted as truths. He called these axioms his 'postulates' and divided them into two groups of five, the first set common to all mathematics, the second specific to geometry.

Some of these postulates seem to be self-explanatory to us, but Euclid operated upon the principle that no axiom could be accepted without proof. Euclid's First Group of Postulates - the Common Notions: Things which are equal to the same thing are also equal to each other If equals are added to equals, the results are equal If equals are subtracted from equals, the remainders are equal Things that coincide with each other are equal to each other The whole is greater than the part From Euclids Elements Book I, Proposition 3( Creative Commons ) The remaining five postulates were related specifically to geometry: A straight line can be drawn between any two points. Any finite straight line can be extended indefinitely in a straight line. For any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center. All right angles are congruent (the same). If a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.

Euclid felt that anybody who could read and understand words could understand his notions and postulates but, to make sure, he included 23 definitions of common words, such as 'point' and 'line', to ensure that there could be no semantic errors. From this basis, he built his entire theory of plane geometry, which has shaped mathematics, science and philosophy for centuries. He proved that it is an impossibility to find the 'largest prime number,' because taking the largest known prime number and adding one to the product of all previous primes and the largest prime will give you another, larger prime number. . Euclid's Influence The reason that Euclid was so influential is that his work is more than just an explanation of geometry or even of mathematics. The way in which he used logic and demanded proof for every theorem shaped the ideas of western philosophers right up until the present day. Great philosopher mathematicians such as Descartes and Newton presented their philosophical works using Euclid's structure and format, moving from simple first principles to complicated concepts. Abraham Lincoln was a fan, and the US Declaration of Independence used Euclid's axiomatic system.

Apart from the Elements, Euclid also wrote works about astronomy, mirrors, optics, perspective and music theory, although many of his works are lost to posterity. Certainly, he can go down in history as one of the greatest mathematicians of all time, and he was certainly one of the giants upon whose shoulders Newton stood. . Who is considered to be the father of geometry? | Reference.com Who is considered to be the father of geometry? A: Quick Answer The Greek mathematician Euclid of Alexandria is considered to be the father of geometry. His mathematical and geometric treatise "Elements" is one of the most influential works in mathematics as well as one of the most successful textbooks ever written. Full Answer Euclid was alive during the reign of Ptolemy I from 323 to 283 B.C. He published "Elements" around 300 B.C., and it soon became the main textbook for teaching geometry. In "Elements," Euclid uses a small set of axioms and deductive logic to construct the framework of what is now known as Euclidean geometry.

"Elements" was one of the first mathematical works to be printed after the invention of the printing press and is thought to be second only to the Bible in the number of editions published. Euclid - Biography, Facts and Pictures Blog Euclid The famous Greek scientist and mathematician Euclid (300 BC) is best known as the author of the Elements, the oldest book consisting of geometrical theorems which is considered to be a standard for logical exposition. Historical Introduction: Not much is known aobut Euclid personally. There have been speculations whether he was a creative mathematician himself or merely collected the work of others. Much data about Euclid is recounted by Proclus, a 5th-century-AD philosopher. Euclid and Archimedes are often considered contemporaries. Euclid’s mathematical education is thought to be obtained from Plato’s pupils in Athens. Advertisements No work about geometrical theorems older than the Elements of Euclid has survived. The Elements superseded all earlier writings. This made it hard for historians to find out the earlier mathematicians whose works were could have been more significant in the development of Greek mathematics than Euclid’s.

The Greek mathematician Thales is known to have discovered a number of theorems in 600 B.C. that appear in the Elements. Eudoxus was given credit for the discovery of the method of exhaustion. Book XII of the Elements uses this method. While earlier mathematics may have been initiated by concrete problems, for instance finding out areas and volumes, by the time of Euclid mathematics had grown into an abstract construction, an intellectual occupation for philosophers as compared to scientists. The Elements The Elements is a collection of 13 books. Each book contains a sequence of propositions or theorems, around 10 to 100, introduced with proper definitions. For instance in Book I, 23 definitions are followed by five postulates, after which five common notions or axioms are included. Other Contributions and Accomplishments: Majority of the work of Euclid is known only through references by other writers. The Data is on plane geometry. The word “data” implies “things given”. The treatise consists of 94 propositions related to the kind of problem where certain data is presented about a figure and from which other data can be deduced.

For instance, if a triangle has one angle given, the rectangle contained by the sides including the angle has to the area of the triangle a given ratio. The Latin and Arabic manuscript translations of the Elements were also done, but it was not until the first printed edition, published in Venice in 1482. The work was very influential in Western education. The first comprehensive English translation was made in 1570. The most important mathematical period in England, around 1700, Greek mathematics was examined most passionately. Euclid was widely respected by all major mathematicians, including Isaac Newton. The developing prepotency of the sciences and mathematics in the 18th and 19th centuries earned Euclid a crucial place in the curriculum of schools and universities throughout the Western world. The Elements was considered educational as a primer in logic. Advertisements Euclid Facts & Biography | Famous Mathematicians Nationality: Greek Famous For: Euclidean Geometry Euclid was a Greek mathematician , known as Euclid of Alexandria, and often referred to as the “Father of Geometry.” In Greek, his name means “Good Glory,” as Euclid is the anglicized version of the Greek name.

He is famous for the treatise Elements, which is considered to catalog and place much of Greek mathematics on a firm foundation. Considered one of the most influential works in the history of mathematics, Euclid’s work was the main textbook for teaching mathematics up until the 20th century. In Elements, the author deduced some geometrical principles based on a small set of axioms. Other themes approached in his work include conic sections, perspective, number theory, spherical geometry and rigor. Euclid’s Life There are few references to Euclid’s life. His education and even birthplace are still in dispute. Some historical references were written by Pappus of Alexandria and Proclus centuries after Euclid’s death (265 BC). Born in approximately 325 BC, Euclid taught mathematics and was the founder of the Alexandrian School of Mathematics. Elements Euclid’s Elements is still recognized as one of the most prominent books on mathematics in history. In it, he pulls together materials from others who studied and researched mathematics before him. He compiled much of that information along with his own original thoughts and research in Elements. It includes information about topics like number theory, algebra, and geometry.

Praise for Elements Some say that Abraham Lincoln admitted he felt greatly influenced by three works: William Shakespeare’s works, the King James Bible, and Euclid’s Elements. It is considered an authoritative masterpiece, laying out carefully and systematically propositions (what can be proven) and axioms and postulates (what can be assumed). The book includes the basic rules of logic, everyday geometric objects’ precise definitions, and the rules of arithmetic. Although being an amazing work in the history of mathematics, it still has its critics. For example, Bertrand Russell, a British philosopher, calls one of Euclid’s propositions “a tissue of nonsense.” However, Euclid’s defenders state that the only issue he had is that he did not study Russell. Euclid’s Other Works Euclid had a few works that survived throughout the years. For instance, On Divisions of Figures was a work that focused on geometrical figures. His work Catoptrics was about mathematical theories of mirrors. There are some other works that have been lost, but there is some record of them, including Conics, Porisms, and Surface Loci, among several others.

Euclid’s Legacy As one of the most well-known mathematicians of all time, there are many forms of math named after him, including Euclidean geometry, the Euclidean number, and the Euclidean algorithm. Famous Mathematicians Euclid Biography - Childhood, Life Achievements & Timeline Scientists Euclid Biography Euclid was a renowned Greek mathematician, known as the âFather of Geometryâ. This biography profiles his childhood, life, works, achievements and timeline. 198 Mathematician - Euclidean Geometry, Euclid's Elements and Euclidean Algorithm Nationality Greece Image Credit Euclid was a great Greek mathematician. Although little is known about his early and personal life, he went on to contribute greatly in the field of mathematics and came to known as the âFather of Geometryâ, Euclid is known to have taught mathematics in Ancient Egypt during the reign of Ptolemy I. He wrote âElementsâ, the most influential mathematical works of all time, which served as the main textbook for teaching mathematics from its publication until the late 19th or early 20th century. Elements aroused interest of the Western World and mathematicians around the globe for over 2000 years.

Euclid used the âsynthetic approachâ towards producing his theorems, definitions and axioms. Apart from being a tutor at the Alexandria library, Euclid coined and structured the different elements of mathematics, such as Porisms, geometric systems, infinite values, factorizations, and the congruence of shapes that went on to contour Euclidian Geometry. His works were heavily influenced by Pythagoras, Aristotle, Eudoxus, and Thales to name a few. Childhood & Early Life Very little information is available about Euclid but it is presumed that he was born around 330 B.C in Tyre. Going by the accounts of certain Arabic authors, he came from a rich background. His father was âNaucratesâ while his grandfather was Zenarchus. It is said that he was a Greek born in Tyre and lived in Damascus throughout his life. However, there is no certain evidence if he was the same person as Euclid of Alexandria is often confused with Euclid of Megara, another man who was a philosopher and lived at the time of Plato.

Since lack of biographical information is rather unusual for this period, many researchers believe that Euclid may have not existed at all and, in fact, his works may have been written by a team of mathematicians who took the name Euclid. But this hypothesis is again rejected by scholars, citing lack of solid evidence. It is also said that he studied in Platoâs ancient school in Athens, a place that was only meant for affluent people. He got his mathematical training from the students of Plato. Career Euclidâs âElementsâ is considered as one of the most influential works in the history of mathematics, from the time of its publication until the late 19th or early 20th century. It actually served as the main textbook for teaching mathematics during this period. In his Elements, he deduced the principles of âEuclidean geometryâ from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. In addition to his most famous work âElementsâ, there are at least five works of Euclid that have survived to this day. They seem to follow the same logical structure as followed in Elements.

They are âDataâ, âOn Divisions of Figures', 'Catoptrics', 'Phaenomena' and 'Optics'. In addition to the abovementioned works, there are a few other works that are attributed to Euclid but have been lost. These works include âConicsâ, âPseudariaâ, âPorismsâ, âSurface Lociâ and âOn the Heavy and the Lightâ. Euclid's Elements âElementsâ is a mathematical and geometric treatise consisting of 13 books written by this great ancient Greek mathematician in Alexandria, Ptolemaic Egypt c. 300 BC. Euclidâs âElementsâ is a collection of definitions, postulates, theorems and constructions and also the mathematical proofs of the propositions. All the 13 books cover Euclidean geometry and the ancient Greek elementary number theory. It also includes geometric algebra, which helps in solving many algebraic problems, including the problem of finding the square root of a number.

The Elements is the second oldest existing Greek mathematical treatise after Autolycus' âOn the Moving Sphereâ and has proven instrumental in the development of logic and modern science. First time printed in 1482 in Venice, âElementsâ is one of the very earliest mathematical works to be printed after the invention of the printing press. It is considered as the most successful and influential textbook ever written and believed to be second only to the holy Bible in the number of editions brought out. It is said more than 1000 editions of âElementsâ were brought out since the time printing came into existence. Other Works âElementsâ was Euclidâs most famous work and continues to influence mathematics even to this day but he wrote a number of other books as well. At least 5 works of Euclid have survived to this day. Data: This book holds 94 propositions and basically deals with the nature and implications of "given" information in geometrical problems. On Divisions of Figures: Another important work of Euclid but survives only partially in Arabic translation.

It resembles a work (3rd century) of âHeron of Alexandriaâ Catoptrics: It is another important work that is related to the mathematical theory of mirrors. J J O'Connor and E F Robertson, however, consider 'Theon of Alexandria' as the real author. Phaenomena: It throws light on spherical astronomy. It is strikingly similar to âOn the Moving Sphereâ by Autolycus of Pitane, who flourished around 310 BC. Optics: This work shares knowledge about theory of perspective and is the earliest surviving Greek treatise on perspective. Apart from the five abovementioned extant works, there are some other works attributed to Euclid, but have been lost. These are âConicsâ, âPorismsâ, âPseudariaâ and âSurface Lociâ. In addition to these, various Arabic sources consider Euclid as author of several works on mechanics. Personal Life & Legacy There is not much information and records relating to Euclidâs personal life but historians believe that he breathed his last around 260 B.C.

His most famous book âThe Elementâ was eventually translated from Arabic to Latin by Campanus. The first printed addition of the same appeared in 1482 in Venice. In 1570, John Dee translated âThe Elementâ in English. Deeâs lectures were able to revive interest in mathematics in England. An Italian mathematician, Girolamo Saccheri, in 1733 tried for years to outdo the works of Euclid but his attempts to refute it went futile as he could not even find a single flaw in Euclidâs theories. Eventually, he gave up and published âEuclid Cleared of Every Flawâ. The legacy that Euclid left behind is immense. He inspired personalities such as Abraham Lincoln, who used to religiously carry âThe Elementsâ with him everywhere and used to quote the genius in his speeches. Euclid influenced great philosophers and mathematicians such as Newton and Descartes who propounded their philosophical works using Elucidâs format and structure. They also moved from simple principles towards complicated concepts just like Elucid.

Top 10 Facts You Did Not Know About Euclid The name âEuclidâ means "renowned, gloriousâ. His book âElementsâ served as the main textbook for teaching mathematics from the time of its publication to until around early 20th century. Most of the other Greek mathematicians from Archimedes onward referred to him as "the author of Elements" and not by name. Some researchers are of the belief that Euclid was not a historical character and that his works were written by a team of mathematicians who collectively took the name Euclid. However, there is little evidence to support this hypothesis. Euclidâs Optics was the first surviving Greek dissertation on the perspective of optics. His work âDivisions of Figuresâ survives only partially in Arabic translation. A detailed biography of Euclid was given by Arabian authors though researchers believe the work to be completely fictitious. Medieval translators and editors often confused Euclid with the philosopher Eukleides of Megara who lived about a century before.

The geometrical system he described in the âElementsâ is referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. It is often said that âElementsâ is one of the most translated, published, and studied of all the books produced in the Western world. Translate this page to Spanish, French, Hindi, Portuguese Pictures of Euclid Famous Mathematicians - The Greatest Mathematicians of All Time Famous Mathematicians Famous Mathematicians Famous Mathematicians Mathematics is a field that many people shy away from, but there are some who had a passion for numbers and making discoveries regarding equations, measurements, and other numerical solutions in history. They looked for ways to understand the world as it relates to numbers and their contributions have been very important for their generation and beyond. Below is a list of names and accomplishments of the greatest mathematicians of all time. You can read through the list and learn more about these people and how they used their mathematical abilities to make their mark on the world. Nationality: German, American Famous For: E=m*c2 Albert Einstein excelled in mathematics early in his childhood. He liked to study math on his own.

He was once quoted as saying, “I never failed in mathematics…before I was fifteen I had mastered differential integral calculus.” Nationality: English Famous For:Mathematical Principles of Natural Philosophy The book of Sir Isaac Newton, Mathematical Principles of Natural Philosophy, became the catalyst to understanding mechanics. He is also the person credited for the development of the binomial theorem. Nationality: Italian Famous For: Fibonacci sequence Heralded as “the most talented western mathematician of the middle ages,” Leonardo Pisano Bigollo is better known as Fibonacci. He introduced the Arabic-Hindu number system to the western world. In his book, Liber Abaci (Book of Calculation), he included a sequence of numbers that are known today as “Fibonacci numbers.” Nationality: Greek Famous For: Father of science & Thales’ theorem Thales used principles of mathematics, specifically geometry, to solve everyday problems. He is considered as the “first true mathematician”. His deductive reasoning principles are applied in geometry that is a product of “Thales’ Theorem.” Nationality: French Famous For: Cartesian coordinate system The “Cartesian coordinate system” in mathematics is named after Rene Descartes.

As a mathematician, he is seen as the father of analytical geometry in addition to explaining “infinitesimal calculus and analysis.” Nationality: Greek Famous For: Greatest mathematician of antiquity Archimedes provided principles and methods used in mathematics today. He provided the exact numerical value of pi, developed a system for large numbers to be expressed, and the method of exhaustion. Nationality: American Famous For: Nash embedding theorem The work of American mathematician John Nash includes studies in differential geometry, game theory, and partial differential equations. He is best known for the Nash embedding theorem. His work in algebraic geometry is also seen as milestone in mathematics. Nationality: French Famous For: Pascal’s Triangle Pascal is recognized for two mathematical areas of study, projective geometry and probability theory. He describes in his paper, Treatise on the Arithmetical Triangle, an easy to understand table of “binomial coefficients” known as Pascal’s Triangle Nationality: Greek Famous For: Father of geometry The earliest known “math books” is one written by Greek mathematician Euclid, Elements is its title. It serve as a textbook to teach geometry and mathematics.

His mathematical system is known as “Euclidean geometry.” Nationality: Indian Famous For: Writing Āryabhaṭīya and the Arya-siddhanta Indian mathematician Aryabhatta’s contribution include his work on providing an approximate value to pi. He likewise touched on the concepts of sine, cosine, and the place-value system. Nationality: Greco-Roman Famous For: Almagest Ptolemy was a mathematician of the highest order. In his book Almagest, or The Mathematical Compilation, Ptolemy provides mathematical theories related to the solar system. Nationality: English Famous For: Work on the Analytical Engine English mathematician Ada Lovelace is recognized as the worlds first computer programmer. Her mathematical skills were evident at an early age. As part of her work, she produced a mathematical algorithm that would be later used in computers. Nationality: British Famous For: Father of computer science Turing’s fame as a mathematician can be attributed to his formulating of algorithms and computations for a computer, the Turing Machine. His mathematical background helped device techniques in code breaking, specifically in world war 2. In 1948 Turing became interested in mathematical biology.

Nationality: Indian Famous For: Landau-Ramanujan constant Ramanujan was a genius in mathematics. He helped expand mathematical theory, particularly in continued fractions, infinite series, mathematical analysis, and number theory. He conducted mathematical research in seclusion. Nationality: African American Famous For: Calculating a solar eclipse Benjamin Banneker was a self-taught mathematician. He used his mathematical skills to predict an eclipse and the seventeen-year cycle of locusts. Nationality: Persian Famous For: Treatise on Demonstration of Problems of Algebra Omar Khayyam wrote one of the most important books in mathematics, Treatise on Demonstration of Problems of Algebra from which most algebraic principles have been drawn from. In the area of geometry, Khayyam worked on the “theory of proportions.” Nationality: Greek Famous For: Sieve of Eratosthenes Eratosthenes provided the concept of a simple algorithm as a way to locate prime numbers. The Sieve of Eratosthenes that has been used to find prime numbers. Nationality: Hungarian Famous For: Operator theory and quantum mechanics The mathematical evaluation of self-replication by John von Neumann came before the DNA model was introduced.

Other mathematical subjects he tackled include the “mathematical formulation of quantum mechanics”, “game theory,” mathematical statistics and mathematical economics. His contribution to the study of the “operator theory” is equally important. Nationality: French Famous For: Fermat’s Last Theorem As an amateur mathematician, de Fermat is given recognition for his work that has led to infinitesimal calculus. He applied the use of “adequality” in explaining his mathematical constructs. De Fermat’s also contributed to the math fields of analytic geometry, differential calculus, and number theory. Nationality: Scottish Famous For: Inventing “logarithms” John Napier is responsible for manufacturing logarithms. It was also he who applied the everyday use of the decimal point in mathematics and arithmetic. Napier’s bones was an abacus created by John. The device was used mainly for multiplication problems. Nationality: German Famous For: Infinitesimal calculus The work of Leibniz on infinitesimal calculus was one completely separate from Isaac Newton. His mathematical notation continues to be in use. He also proposed the mathematical principle known as the Transcendental Law of Homogeneity. His refining of the binary system has become foundational in mathematics.

Nationality: Proving “Fermat’s Last Theorem” Famous For: British Andrew Wiles was successful in proving “Fermat’s Last Theorem”. He also used the “Iwasawa theory” to identify elliptic curves using its complex multiplication system. Wiles, with a colleague, worked on rational numbers under the “Iwasawa theory”. Nationality: German Famous For: Hilbert’s basis theorem In cumulative algebra, the use of “Hilbert’s basis theory” has produced varying results. David Hilbert explored and improved on ideas such as “axiomatization of geometry” and the “invariant theory.” Functional analysis, a branch of mathematical analysis, is based on the formulation of “Hilbert’s spaces theory.” Nationality: Swiss Famous For: Bernoulli principle Nationality: Italian Famous For: Father of accounting Fifteenth century friar and mathematician Luca Pacioli developed an accounting or bookkeeping methods that are still in use today. Because of this, Pacioli is viewed by many as the “father of accounting.” Nationality: German Famous For: Inventor of set theory One of the basic theories in mathematics is the set theory, thanks to the work of Georg Cantor.

He helped define the importance of the “one-to-one correspondence” principle as well as introduce cardinal and ordinal numbers. Nationality: English Famous For: Boolean algebra George Boole and his ideas on mathematics were in the field of algebraic logic and differential equations. He is the source of what is known as “Boolean logic” in algebra. This and other mathematical concepts are part of his bookThe Laws of Thought. Nationality: French Famous For: Theory of Equations Galois worked on abstract algebra and the theory of equations. He also set forth a solution to the polynomial equation which is know as the “Galois theory.” Nationality: French Famous For: Sophie Germain prime numbers Sophie Germain worked extensively in the mathematical field of number theory and differential geometry. She helped lay possible solutions to “Ferrats Last Theorem.” Sophie’s work with number theory earned her recognition and having numbers named after her, “Sophie Germain prime.” Nationality: German Famous For: Abstract algebra Emmy Noether and her work on abstract algebra makes her one of the most important mathematicians of her time. She introduced theories on algebraic variants and number fields.

In Noether’s paper, Theory of Ideals in Ring Domains, she presented her ideas on the “commutative ring”, an abstract algebra sub area. Geometry History - Interesting Facts & Information Logic Puzzles Money Addition Subtraction Multiplication Division Counting Problem Solving Sudoku Board Games Memory Fractions Probability Geometry History Enjoy reading some geometry history while learning where many of our modern ideas came from. Find interesting facts and information related to works produced by the Ancient Egyptians, Babylonians, Greeks and other famous mathematicians. Read on and enjoy learning a brief history of geometry before taking a look at all our other interesting information devoted to the wonderful world of mathematics. The word ‘geometry’ comes from the Greek words ‘geo’, meaning earth, and ‘metria’, meaning measure. Along with arithmetic, geometry was one of the two fields of pre-modern mathematics. Ancient Egyptians used geometry principles as far back as 3000 BC, using equations to approximate the area of circles among other formulas. Babylonians measured the circumference of a circle as approximately 3 times the diameter, which is fairly close to today’s measurement which uses the value of Pi (around 3.14).

A Greek mathematician named Euclid who lived around the year 300 BC is often referred to as the ‘Father of Geometry’ for his amazing geometry works that included the influential ‘Elements’, which remained the main textbook for teaching mathematics until around the early 20th century. Greeks constructed aesthetically pleasing buildings and artworks based on the golden ratio of approximately 1.618. Greek philosopher and mathematician Pythagoras lived around the year 500 BC and is known for his Pythagorean theorem relating to the three sides of a right angle triangle: a² + b² = c² Archimedes of Syracuse lived around the year 250 BC and played a large role in the history of geometry including a method for determining the volume of objects with irregular shapes. The compass and straight edge were powerful tools in the advancement of geometry, allowing the construction of various lengths, angles and geometric shapes. Modern day geometry has made developments in a number of areas, including those that make use of the raw computing power of today’s computers.

Question: Which Greek mathematician is known as the Father of Geometry?
Answer: EUCLID