Not to be confused with Pythagoras's constant or height of a field.
In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p(K) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.
A Pythagorean field is a field with Pythagoras number 1: that is, every sum of squares is already a square.
mathematics, the Pythagorasnumber or reduced height of a field describes the structure of the set of squares in the field. The Pythagorasnumber p(K) of a field...
Pythagoras of Samos (Ancient Greek: Πυθαγόρας ὁ Σάμιος, romanized: Pythagóras ho Sámios, lit. 'Pythagoras the Samian', or simply Πυθαγόρας; Πυθαγόρης...
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...
and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in...
first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced...
divulging it. The square root of two is occasionally called Pythagoras'snumber or Pythagoras's constant, for example by Conway & Guy (1996). In ancient...
traditional numerology. For example, in his 1997 book Numerology: Or What Pythagoras Wrought (Dudley 1997), mathematician Underwood Dudley uses the term to...
Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in...
after Pythagoras, the ancient Greek philosopher, mystic, mathematician, and music theorist. Pythagoreanism – the system of philosophy of Pythagoras and...
philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the number 1 differently than larger numbers, sometimes even not as a number at all...
divulging it. The square root of two is occasionally called "Pythagoras' number" or "Pythagoras' Constant", for example Conway & Guy (1996). The ancient Greeks...
Verses Of Pythagoras And Other Pythagorean Fragments. Theosophical Publishing House. Joost-Gaugier, Christiane L. (2007). Measuring Heaven: Pythagoras and his...
be exactly determined. Around 500 BC, the Greek mathematicians led by Pythagoras also realized that the square root of 2 is irrational. The Middle Ages...
52-card decks. According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the only number to equal the sum of all the...
{x^{2}+y^{2}}}.} By Pythagoras' theorem, | z | {\displaystyle |z|} is the distance from the origin to the point representing the complex number z in the complex...
According to legend, Pythagoras discovered the foundations of musical tuning by listening to the sounds of four blacksmith's hammers, which produced consonance...
A Pythagorean prime is a prime number of the form 4 n + 1 {\displaystyle 4n+1} . Pythagorean primes are exactly the odd prime numbers that are the sum...
disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus...
attributed to the ancient Greek mathematician Pythagoras (570–495 BC). It is also called the Table of Pythagoras in many languages (for example French, Italian...
Pythagoras was one of many Greek philosophers. He lived his life on the island Samos and is known for his contributions to mathematics. Pythagoras taught...
in which every sum of two squares is a square: equivalently it has Pythagorasnumber equal to 1. A Pythagorean extension of a field F {\displaystyle F}...
also the biographer of the Greek mystic, philosopher, and mathematician Pythagoras. In addition to his philosophical contributions, his Protrepticus is important...
subtle details or allusions; among those commonly identified are Socrates, Pythagoras, Archimedes, Heraclitus, Averroes, and Zarathustra. Additionally, Italian...
found in the spirals of nature's designs, quoting Pythagoras: "Everything is arranged according to number and mathematical shape." Donald then learns that...
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