Question: Information: - A triangular number or triangle number counts the objects that can form an equilateral triangle, as in the diagram on the right. The th triangular number is the number of dots composing a triangle with dots on a side, and is equal to the sum of the natural numbers from 1 to . The sequence of triangular numbers , starting at the 0th triangular number, is - Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. - In geometry, an octagon (from the Greek "oktagnon", "eight angles") is an eight-sided polygon or 8-gon. - In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. - In planar geometry, an angle is the figure formed by two rays, called the "sides" of the angle, sharing a common endpoint, called the "vertex" of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. - An octagonal number is a figurate number that represents an octagon . The octagonal number for n is given by the formula 3n2 - 2n , with n > 0 . The first few octagonal numbers are : 1 , 8 , 21 , 40 , 65 , 96 , 133 , 176 , 225 , 280 , 341 , 408 , 481 , 560 , 645 , 736 , 833 , 936 ( sequence A000567 in OEIS ) Octagonal numbers can be formed by placing triangular numbers on the four sides of a square . To put it algebraically , the n - th octagonal number is x_n = n ^ 2 + 4 \ sum -- ( k = 1 ) ^ ( n - 1 ) k = 3n ^ 2 - 2n . The octagonal number for n can also be calculated by adding the square of n to twice the ( n - 1 ) th pronic number . Octagonal numbers consistently alternate parity . Octagonal numbers are occasionally referred to as '' star numbers , '' though that term is more commonly used to refer to centered dodecagonal numbers . - The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean - The Multinational Aircrew Electronic Warfare Tactics Facility Polygone - POLYGON is an Electronic Warfare Tactics Range located on the border between Germany and France. It is a tri-national facility operated by France, Germany and the United States. What entity does 'octagonal number' has the relation 'subclass of' with?
Answer: polygonal number

input: Please answer the following: Information: - Poetry (the term derives from a variant of the Greek term, "poiesis", "making") is a form of literature that uses aesthetic and rhythmic qualities of languagesuch as phonaesthetics, sound symbolism, and metreto evoke meanings in addition to, or in place of, the prosaic ostensible meaning. - De rerum natura ( Latin : ( de rer natura ) ; On the Nature of Things ) is a first - century BC didactic poem by the Roman poet and philosopher Lucretius ( c. 99 BC -- c. 55 BC ) with the goal of explaining Epicurean philosophy to a Roman audience . The poem , written in some 7,400 dactylic hexameters , is divided into six untitled books , and explores Epicurean physics through richly poetic language and metaphors . Lucretius presents the principles of atomism ; the nature of the mind and soul ; explanations of sensation and thought ; the development of the world and its phenomena ; and explains a variety of celestial and terrestrial phenomena . The universe described in the poem operates according to these physical principles , guided by fortuna , '' chance , '' and not the divine intervention of the traditional Roman deities . - A poet is a person who writes poetry. Poets may describe themselves as such or be described as such by others. A poet may simply be a writer of poetry, or may perform their art to an audience. - Epicureanism is a system of philosophy based upon the teachings of the ancient Greek philosopher Epicurus, founded around 307 BC. Epicurus was an atomic materialist, following in the steps of Democritus. His materialism led him to a general attack on superstition and divine intervention. Following Aristippusabout whom very little is knownEpicurus believed that what he called "pleasure" was the greatest good, but that the way to attain such pleasure was to live modestly, to gain knowledge of the workings of the world, and to limit one's desires. This would lead one to attain a state of tranquility ("ataraxia") and freedom from fear as well as an absence of bodily pain ("aponia"). The combination of these two states constitutes happiness in its highest form. Although Epicureanism is a form of hedonism insofar as it declares pleasure to be its sole intrinsic goal, the concept that the absence of pain and fear constitutes the greatest pleasure, and its advocacy of a simple life, make it very different from "hedonism" as it is colloquially understood. - Titus Lucretius Carus (15 October 99 BC c. 55 BC) was a Roman poet and philosopher. His only known work is the epic philosophical poem "De rerum natura" about the tenets and philosophy of Epicureanism, and which is usually translated into English as "On the Nature of Things". Lucretius has been credited with originating the concept of the three-age system which was formalised from 1834 by C. J. Thomsen. What entity does 'de rerum natura' has the relation 'movement' with?
++++++++++
output:
epicureanism