Thales' writings have not survived and are known only second-hand. He is credited with being first to use axioms and deductive proofs, so his influence on Plato and Euclid may be enormous; he is generally credited with much of Books I and II of Euclid's Elements. If you insist on a single winner then India might be it.

And, finally, we compare 6 to 3 to conclude: Today, Egyptian fractions lead to challenging number theory problems with no practical applications, but they may have had practical value for the Egyptians. Although Archimedes didn't develop differentiation integration's inverseMichel Chasles credits him along with Kepler, Cavalieri, and Fermat, who all lived more than 18 centuries later as one of the four who developed calculus before Newton and Leibniz.

Maxwell's Equations are Unified Field Equations. Thabit shows how to construct a regular heptagon; it may not be clear whether this came from Archimedes, or was fashioned by Thabit by studying Archimedes' angle-trisection method.

So in order to use this you have to be certain that all the important information is in the lower bits. Pythagoras was very interested in astronomy and seems to have been the first man to realize that the Earth was a globe similar to the other planets.

The Trouble with Tensors, a critique of the tensor and the tensor field as used by GR. Although some regard these paradoxes as simple fallacies, they have been contemplated for many centuries. For his texts and theorems, he may be called the "Father of Trigonometry;" he was first to properly state and prove several theorems of planar and spherical trigonometry including the Law of Sines, and the spherical Law of Tangents.

This is because the curve crosses the x axis at 1 and next at 2, so the distance from the origin has doubled, but the next crossing is not at 4 which would mean another doubling as required for a logarithmic spiral but at 5. He is famous for his prime number Sieve, but more impressive was his work on the cube-doubling problem which he related to the design of siege weapons catapults where a cube-root calculation is needed.

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.

Al-Biruni's contemporary Avicenna was not particularly a mathematician but deserves mention as an advancing scientist, as does Avicenna's disciple Abu'l-Barakat al-Baghdada, who lived about a century later.

Many of his works have survived only in a fragmentary form, and the proofs were completely lost. Another difference is that the Hindus had nine distinct digit symbols to go with their zero, while earlier place-value systems built up from just two symbols: I also show Newton's close pass to the Lagrangian.

Constructing the eight circles each tangent to three other circles is especially challenging, but just finding the two circles containing two given points and tangent to a given line is a serious challenge. Mathematicians find uses for complex numbers in solving equations: Other early cultures also developed some mathematics.

So when he refers to a hash function, he means something that both hashes the incoming key, and assigns it to a slot in the table.

None of these seems difficult today, but it does seem remarkable that they were all first achieved by the same man. Find a simpler form for G 1,3,i solely in terms of Fibonacci numbers in terms of Lucas numbers Make a table of a values rows against b values columnseach from 0 to 4, and fill in the entries in the table with a simple formula for G a,b,i.

Hippocrates of Chios ca BC Greek domain Hippocrates no known relation to Hippocrates of Cos, the famous physician wrote his own Elements more than a century before Euclid.

Hipparchus is called the "Father of Trigonometry"; he developed spherical trigonometry, produced trig tables, and more. Although the physical sciences couldn't advance until the discoveries by great men like Newton and Lavoisier, Aristotle's work in the biological sciences was superb, and served as paradigm until modern times.

Ptolemy perfected or, rather, complicated this model even further, introducing 'equants' to further fine-tune the orbital speeds; this model was the standard for 14 centuries. Given any numbers a and b the Pythagoreans were aware of the three distinct means: The Chinese used a form of decimal abacus as early as BC; if it doesn't qualify, by itself, as a "decimal system" then pictorial depictions of its numbers would.

Try to convert the "by-hand method" in code. Eudoxus has been quoted as saying "Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance. Other tables, like google:: Click here for a longer List of including many more 20th-century mathematicians.

The Universal Gravitational Constant.

He had great historical influence in Europe, India and Persia, at least if credited also with Ptolemy's influence. He was a great linguist; studied the original works of Greeks and Hindus; is famous for debates with his contemporary Avicenna; studied history, biology, mineralogy, philosophy, sociology, medicine and more; is called the Father of Geodesy and the Father of Arabic Pharmacy; and was one of the greatest astronomers.

I continue my previous analyses of the General Theory, going straight the original papers of Einstein. He deliberately emphasized the beauty of pure, rather than applied, mathematics, saying his theorems were "worthy of acceptance for the sake of the demonstrations themselves.

The Vedics understood relationships between geometry and arithmetic, developed astronomy, astrology, calendars, and used mathematical forms in some religious rituals.

Angular Velocity and Angular Momentum. The Virial Theorem is False. A Time-line for the History of Mathematics (Many of the early dates are approximates) This work is under constant revision, so come back later. Please report any errors to me at [email protected] What I Wish I Knew When Learning Haskell Version Stephen Diehl (@smdiehl)This is the fourth draft of this document.

License. This code and text are dedicated to the public domain. 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.

I'm a learning programmer and I've run into a bit of a jumble. 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).

Sep 04, · How to Calculate the Fibonacci Sequence Two Methods: Using a Table Using Binet's Formula and the Golden Ratio Community Q&A The Fibonacci sequence is a pattern of numbers generated by summing the previous two numbers in the sgtraslochi.com: K.

AVAILABLE BOOKS Click here to order any book THE GREATEST STANDING ERRORS IN PHYSICS. AND MATHEMATICS. by Miles Mathis Painting Experiment with an Air Pump by Joseph Wright of Derby,National Gallery, London email me at [email protected] go to my art site.

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A Formula for the n-th Fibonacci number