New SILVER proof 🅰️ GREECE 6 Euro 2018 GRECE 🅰️100 YEARS MATHEMATICAL SOCIETY

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Seller: ara*mis ✉️ (2,016) 100%, Location: Themost beautiful country in the world , GR, Ships to: WORLDWIDE, Item: 254016751491 New SILVER proof 🅰️ GREECE 6 Euro 2018 GRECE 🅰️100 YEARS MATHEMATICAL SOCIETY. The item on the pictures is the one that you will receive. Look carrefully and judge for your self for the quallity and the grade. S&h is $9.90 for all the world. Registered mail. BID WITH CONFIDENCE. . SELLER with 100% POSITIVE FEEDBACK. SILVER PROOF. GREECE 6 EURO 2018 100 YEARS GREEK MATHEMATICAL SOCIETY. YEAR OF MATHEMATICS. Original Proof coin from the National bank of Greece. 1500 Coins Mintage. 925° SILVER 10.00 Grams 28.50 mm Diameter Comes with Certificate Of Authenticity (C.O.A.) and Original Box. The Hellenic Mathematical Society (HMS) (Greek: Ελληνική Μαθηματική Εταιρεία) is a learned society which promotes the study of mathematics in Greece. It was founded in 1918, and published the Bulletin of the Greek Mathematical Society. It is a member of the European Mathematical Society.[1] External links Hellenic Mathematical Society Official site Pi Part of a series of articles on the mathematical constant π 3.1415926535897932384626433... Uses Area of a circle Circumference Use in other formulae Properties Irrationality Transcendence Value Less than 22/7 Approximations Memorization People Archimedes Liu Hui Zu Chongzhi Aryabhata Madhava Ludolph van Ceulen Seki Takakazu Takebe Kenko William Jones John Machin William Shanks Srinivasa Ramanujan John Wrench Chudnovsky brothers Yasumasa Kanada History Chronology Book In culture Legislation Pi Day Related topics Squaring the circle Basel problem Six nines in π Other topics related to π vte The number π (/paɪ/) is a mathematical constant. Originally defined as the ratio of a circle's circumference to its diameter, it now has various equivalent definitions and appears in many formulas in all areas of mathematics and physics. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi". It is also called Archimedes' constant. Being an irrational number, π cannot be expressed as a common fraction (equivalently, its decimal representation never ends and never settles into a permanently repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed. In particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date, no proof of this has been discovered. Also, π is a transcendental number; that is, it is not the root of any polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. Ancient civilizations required fairly accurate computed values to approximate π for practical reasons, including the Egyptians and Babylonians. Around 250 BC the Greek mathematician Archimedes created an algorithm for calculating it. In the 5th century AD Chinese mathematics approximated π to seven digits, while Indian mathematics made a five-digit approximation, both using geometrical techniques. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics.[1][2] In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits after the decimal point.[3] Practically all scientific applications require no more than a few hundred digits of π, and many substantially fewer, so the primary motivation for these computations is the quest to find more efficient algorithms for calculating lengthy numeric series, as well as the desire to break records.[4][5] The extensive calculations involved have also been used to test supercomputers and high-precision multiplication algorithms. Because its most elementary definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses, and spheres. In more modern mathematical analysis, the number is instead defined using the spectral properties of the real number system, as an eigenvalue or a period, without any reference to geometry. It appears therefore in areas of mathematics and the sciences having little to do with the geometry of circles, such as number theory and statistics, as well as in almost all areas of physics. The ubiquity of π makes it one of the most widely known mathematical constants both inside and outside the scientific community. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines. Attempts to memorize the value of π with increasing precision have led to records of over 70,000 digits. Name The symbol used by mathematicians to represent the ratio of a circle's circumference to its diameter is the lowercase Greek letter π, sometimes spelled out as pi, and derived from the first letter of the Greek word perimetros, meaning circumference.[6] In English, π is pronounced as "pie" (/paɪ/, py).[7] In mathematical use, the lowercase letter π (or π in sans-serif font) is distinguished from its capitalized and enlarged counterpart ∏, which denotes a product of a sequence, analogous to how ∑ denotes summation. The choice of the symbol π is discussed in the section Adoption of the symbol π.Definition The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π. π is commonly defined as the ratio of a circle's circumference C to its diameter d:[8] π = C d {\displaystyle \pi ={\frac {C}{d}}} The ratio C/d is constant, regardless of the circle's size. For example, if a circle has twice the diameter of another circle it will also have twice the circumference, preserving the ratio C/d. This definition of π implicitly makes use of flat (Euclidean) geometry; although the notion of a circle can be extended to any curved (non-Euclidean) geometry, these new circles will no longer satisfy the formula π = C/d.[8] Here, the circumference of a circle is the arc length around the perimeter of the circle, a quantity which can be formally defined independently of geometry using limits, a concept in calculus.[9] For example, one may directly compute the arc length of the top half of the unit circle, given in Cartesian coordinates by the equation x2 + y2 = 1, as the integral:[10] π = ∫ − 1 1 d x 1 − x 2 . {\displaystyle \pi =\int _{-1}^{1}{\frac {dx}{\sqrt {1-x^{2}}}}.} An integral such as this was adopted as the definition of π by Karl Weierstrass, who defined it directly as an integral in 1841.[11] Definitions of π such as these that rely on a notion of circumference, and hence implicitly on concepts of the integral calculus, are no longer common in the literature. Remmert (1991) explains that this is because in many modern treatments of calculus, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to have a definition of π that does not rely on the latter. One such definition, due to Richard Baltzer,[12] and popularized by Edmund Landau,[13] is the following: π is twice the smallest positive number at which the cosine function equals 0.[8][10][14] The cosine can be defined independently of geometry as a power series,[15] or as the solution of a differential equation.[14] In a similar spirit, π can be defined instead using properties of the complex exponential, exp(z), of a complex variable z. Like the cosine, the complex exponential can be defined in one of several ways. The set of complex numbers at which exp(z) is equal to one is then an (imaginary) arithmetic progression of the form: { … , − 2 π i , 0 , 2 π i , 4 π i , … } = { 2 π k i ∣ k ∈ Z } {\displaystyle \{\dots ,-2\pi i,0,2\pi i,4\pi i,\dots \}=\{2\pi ki\mid k\in \mathbb {Z} \}} and there is a unique positive real number π with this property.[10][16]A more abstract variation on the same idea, making use of sophisticated mathematical concepts of topology and algebra, is the following theorem:[17] there is a unique (up to automorphism) continuous isomorphism from the group R/Z of real numbers under addition modulo integers (the circle group) onto the multiplicative group of complex numbers of absolute value one. The number π is then defined as half the magnitude of the derivative of this homomorphism.[18] A circle encloses the largest area that can be attained within a given perimeter. Thus the number π is also characterized as the best constant in the isoperimetric inequality (times one-fourth). There are many other, closely related, ways in which π appears as an eigenvalue of some geometrical or physical process; see below. Mathematics Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.[a] Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity,[1] structure,[2] space,[1] and change.[3][4][5] Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Archimedes used the method of exhaustion to approximate the value of pi. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics.[15] Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His textbook Elements is widely considered the most successful and influential textbook of all time.[16] The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.[17] He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.[18] Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC),[19] trigonometry (Hipparchus of Nicaea (2nd century BC),[20] and the beginnings of algebra (Diophantus, 3rd century AD).[21] During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. EtymologyThe word mathematics comes from Ancient Greek μάθημα (máthēma), meaning "that which is learnt",[23] "what one gets to know", hence also "study" and "science". The word for "mathematics" came to have the narrower and more technical meaning "mathematical study" even in Classical times.[24] Its adjective is μαθηματικός (mathēmatikós), meaning "related to learning" or "studious", which likewise further came to mean "mathematical". In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē)
  • Year: 2018
  • Grade: proof
  • Denomination: Euro
  • Country/Region of Manufacture: Greece
  • Circulated/Uncirculated: Uncirculated
  • Certification: Uncertified
  • Composition: Silver

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