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Proof Without Words
In mathematics, a proof without words (or visual proof) is an illustration of an identity (mathematics), identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more Mathematical beauty, elegant than formal or rigour, mathematically rigorous proofs due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable. A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof. Examples Sum of odd numbers The statement that the sum of all positive parity (mathematics), odd numbers up to 2''n'' − 1 is a square number, perfect square—more specifically, the perfect square ''n''2—can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomachus Theorem 3D
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected scholar o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
