Encyclopedia - Pythagoras: Encyclopedia Ii - Pythagoras - Biography
Pythagoras was born on the island of Samos, off the coast of Asia Minor. He was born to Pythais (a native of Samos) and Mnesarchus (a mer...   » Read the article

Encyclopedia - Pythagoras: Encyclopedia Ii - Pythagoras - Pythagoreans
Pythagoras' followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians who had an ...   » Read the article

Encyclopedia - Pythagoras: Encyclopedia Ii - Pythagoras - Scientific Contributions
Some consider Pythagoras the pupil of Anaximander and some ancient sources tell of his visiting, in his twenties, the philosopher Thales,...   » Read the article

Encyclopedia - Pythagoras: Encyclopedia - Pythagoras
Pythagoras (approximately 569 BCE – 475 BCE, Greek: Πυθαγόρας) was an Ionian mathematician and philosopher, founder of the my...   » Read the article

Encyclopedia - Pythagoreanism: Encyclopedia - Pythagoreanism
Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were ...   » Read the article

Encyclopedia - Irrational Number: Encyclopedia Ii - Irrational Number - History
The earliest known use of irrational numbers was in the Indian Sulba Sutras composed between 800-500 BC. The first proof of irrational nu...   » Read the article

Encyclopedia - Pythagoreanism: Encyclopedia Ii - Pythagoreanism - Influence
The word 'vegetarian' was coined in 1847 when the British Vegetarian Society was formed. Before this, vegetarians were known as Pythagore...   » Read the article

Encyclopedia - Square Root: Encyclopedia Ii - Square Root - Computation
Pocket calculators typically implement good routines to compute the exponential function and the natural logarithm, and then compute the ...   » Read the article

Encyclopedia - Square Root: Encyclopedia Ii - Square Root - Square Roots Of Matrices And Operators
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we th...   » Read the article

Encyclopedia - Pythagoreanism: Encyclopedia Ii - Pythagoreanism - Pythagorean Cosmology
Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. In the area of cosmology there is less agreement a...   » Read the article

Encyclopedia - Square Root: Encyclopedia Ii - Square Root - Square Roots Of Matrices And Operators
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we th...   » Read the article

Encyclopedia - Square Root: Encyclopedia Ii - Square Root - Square Roots Of Complex Numbers
To every non-zero complex number z there exist precisely two numbers w such that w2 = z. The usual definition of √z is as follows: if z...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Alternate Forms
The formula can be expanded recursively to obtain a continued fraction for the golden ratio: and its reciprocal: Note that the suc...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Definition
Two quantities are said to be in the golden ratio, if "the whole (i.e., the sum of the two parts) is to the larger part as the larger par...   » Read the article

Encyclopedia - List Of Philosophers: Encyclopedia Ii - List Of Philosophers - Notes
Note O: - For more information about this person's contribution to philosophy, see his/her entry in The Oxford Companion to Philosophy....   » Read the article

Encyclopedia - Square Root: Encyclopedia Ii - Square Root - Infinitely Nested Square Roots
Under certain conditions infinitely nested radicals such as represent rational numbers. This rational number can be found by realizing...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - A Startlingly Quick Proof Of Irrationality
Recall that we denoted the "larger part" by a and the "smaller part" by b, and concluded that This gives a startlingly quick proof tha...   » Read the article

Encyclopedia - Irrational Number: Encyclopedia Ii - Irrational Number - Logarithms
Perhaps the numbers most easily proved to be irrational are certain logarithms. Here is a proof by reductio ad absurdum that log23 is irr...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Alternate Forms
The formula can be expanded recursively to obtain a continued fraction for the golden ratio: and its reciprocal: Note that the suc...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Mathematical Uses
The number φ turns up frequently in geometry, in particular in figures involving pentagonal symmetry. For instance the ratio of a regula...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Decimal Expansion
(sequence A001622 in OEIS) 1.6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227052604 6281890244 9707207204 189391...   » Read the article

Encyclopedia - Irrational Number: Encyclopedia Ii - Irrational Number - Transcendental And Algebraic Irrationals
Almost all irrational numbers are transcendental and all transcendental numbers are irrational: the article on transcendental numbers lis...   » Read the article

Encyclopedia - Irrational Number: Encyclopedia Ii - Irrational Number - Decimal Expansions
It is often erroneously assumed that mathematicians define "irrational number" in terms of decimal expansions, calling a number irrationa...   » Read the article

Encyclopedia - Irrational Number: Encyclopedia Ii - Irrational Number - The Square Root Of 2
One proof of the irrationality of the square root of 2 is the following reductio ad absurdum. The proposition is proved by assuming the n...   » Read the article

Encyclopedia - Golden Ratio: Encyclopedia Ii - Golden Ratio - Aesthetic Uses
It has been claimed that the ancient Egyptians knew the golden ratio because ratios close to the golden ratio may be found in the positio...   » Read the article

Article - Popular Pages Sitemap Vi - H
This is a sitemap for Popular Pages VI - H . Click on a link and you will find multiple definitions and articles related to the word. ...   » Read the article