Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidiasphi, to symbolize the golden ratio. The golden ratio has been claimed to have held a special fascination for at least 2, years, although without reliable evidence.

This is primarily a list of Greatest Mathematicians of the Past, but I use birth as an arbitrary cutoff, and two of the "Top " are still alive now.

Click here for a longer List of including many more 20th-century mathematicians. Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings or an error in any of the biographies. Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different.

I'm sure I've overlooked great mathematicians who obviously belong on this list. Please e-mail and tell me! Following are the top mathematicians in chronological birth-year order.

By the way, the ranking assigned to a mathematician will appear if you place the cursor atop the name at the top of his mini-bio. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic.

The markings include six prime numbers 5, 7, 11, 13, 17, 19 in order, though this is probably coincidence. The advanced artifacts of Egypt's Old Kingdom and the Indus-Harrapa civilization imply strong mathematical skill, but the first written evidence of advanced arithmetic dates from Sumeria, where year old clay tablets show multiplication and division problems; the first abacus may be about this old.

By years ago, Mesopotamian tablets show tables of squares, cubes, reciprocals, and even logarithms and trig functions, using a primitive place-value system in base 60, not Babylonians were familiar with the Pythagorean Theorem, solutions to quadratic equations, even cubic equations though they didn't have a general solution for theseand eventually even developed methods to estimate terms for compound interest.

The Greeks borrowed from Babylonian mathematics, which was the most advanced of any before the Greeks; but there is no ancient Babylonian mathematician whose name is known.

Also at least years ago, the Egyptian scribe Ahmes produced a famous manuscript now called the Rhind Papyrusitself a copy of a late Middle Kingdom text. It showed simple algebra methods and included a table giving optimal expressions using Egyptian fractions.

Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. The Pyramids demonstrate that Egyptians were adept at geometry, though little written evidence survives. Babylon was much more advanced than Egypt at arithmetic and algebra; this was probably due, at least in part, to their place-value system.

But although their base system survives e. The Vedics understood relationships between geometry and arithmetic, developed astronomy, astrology, calendars, and used mathematical forms in some religious rituals. The earliest mathematician to whom definite teachings can be ascribed was Lagadha, who apparently lived about BC and used geometry and elementary trigonometry for his astronomy.

Apastambha did work summarized below; other early Vedic mathematicians solved quadratic and simultaneous equations. Other early cultures also developed some mathematics. The ancient Mayans apparently had a place-value system with zero before the Hindus did; Aztec architecture implies practical geometry skills.

Ancient China certainly developed mathematics, in fact the first known proof of the Pythagorean Theorem is found in a Chinese book Zhoubi Suanjing which might have been written about BC. Thales may have invented the notion of compass-and-straightedge construction.

Several fundamental theorems about triangles are attributed to Thales, including the law of similar triangles which Thales used famously to calculate the height of the Great Pyramid and "Thales' Theorem" itself: The other "theorems" were probably more like well-known axioms, but Thales proved Thales' Theorem using two of his other theorems; it is said that Thales then sacrificed an ox to celebrate what might have been the first mathematical proof in Greece.

Thales was also an astronomer; he invented the day calendar, introduced the use of Ursa Minor for finding North, invented the gnomonic map projection the first of many methods known today to map part of the surface of a sphere to a plane, and is the first person believed to have correctly predicted a solar eclipse.

His theories of physics would seem quaint today, but he seems to have been the first to describe magnetism and static electricity. Aristotle said, "To Thales the primary question was not what do we know, but how do we know it.

It is said he once leased all available olive presses after predicting a good olive season; he did this not for the wealth itself, but as a demonstration of the use of intelligence in business.

Thales' writings have not survived and are known only second-hand. Since his famous theorems of geometry were probably already known in ancient Babylon, his importance derives from imparting the notions of mathematical proof and the scientific method to ancient Greeks.

Thales' student and successor was Anaximander, who is often called the "First Scientist" instead of Thales: Anaximander is famous for astronomy, cartography and sundials, and also enunciated a theory of evolution, that land species somehow developed from primordial fish!I'm a learning programmer and I've run into a bit of a jumble.

By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. PROBLEM POSING. Students have asked me, on several occasions, "Is there any math after calculus?" These students have been given the impression that the world of mathematics is both finite and linear (the classic algebra-through-calculus sequence). all getting closer and closer to the Golden Ratio. And that is why Fibonacci Numbers are very common in plants. 1, 2, 3, 5, 8, 13, 21, etc occur in an amazing number of places.

I am asked to write a program that will compute and display Fibonacci's Sequence by a user inputted start number and end number (ie. startNumber = 20 endNumber = and it will display only the numbers between that range). GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest number that divides both of them.

For example GCD of 20 and 28 is 4 and GCD of 98 and 56 is and, in general, a 2 + b 2 = c 2, where a 2 = b + yunusemremert.com is a special class of Pythagorean triples (see below Pythagorean triples).Besides these, the Greeks also studied numbers having pentagonal, hexagonal, and other shapes.

GCD of two numbers is the largest number that divides both of them. A simple way to find GCD is to factorize both numbers and multiply common factors.

Basic Euclidean Algorithm for GCD The algorithm is based on below facts. If we subtract smaller number from larger (we reduce larger number), GCD.

Problem H n is a Fibonacci number if and only if 5n 2 +4 or 5n is a square posed and solved by I Gessel in Fibonacci Quarterly () vol 10, page The method above needs to square the number n being tested and then has to check the new number 5 n 2 ± 4 is a square number.

This sequence of Fibonacci numbers arises all over mathematics and also in nature. However, if I wanted the th term of this sequence, it would take lots of intermediate calculations with the recursive formula to get a result.

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A Formula for the n-th Fibonacci number