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November 18, 2021

Nicomachus

Caption: Plato (left) and Nicomachus (right), as inventors of music, from a 12th-century manuscript

Nicomachus of Gerasa[1] (Greek: Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist,[2] best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek. He was born in Gerasa, in the Roman province of Syria (now Jerash, Jordan). He was a Neopythagorean, who wrote about the mystical properties of numbers.[3][4]

 

Caption: Nicomachus’s theorem states that a square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes

In number theory, the sum of the first n cubes is the square of the nth triangular number. That is,

{\displaystyle 1^{3}+2^{3}+3^{3}+\cdots +n^{3}=\left(1+2+3+\cdots +n\right)^{2}.}

 

The same equation may be written more compactly using the mathematical notation for summation:

{\displaystyle \sum _{k=1}^{n}k^{3}={\bigg (}\sum _{k=1}^{n}k{\bigg )}^{2}.}

This identity is sometimes called Nicomachus’s theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE).

About Author

Daniel is the Founder and CEO of planksip®, which has a registered Canadian trademark describing a methodology of promoting and propagating thought concepts and intellectual property for non-fiction authors and Academics. As a Science and Philosophy writer, Daniel is an active blogger, author and father of two living on Vancouver Island. As self-described "Flâneur", Daniel draws inspiration for his epistemological schema on topics related to Newtonian Giants, Artificial Intelligence, Free Will, Philosophy, Psychology, Mathematics and Quantum Physics. Phrases like, "driven by Data and propagated through the Praxis of planksip®", summarize his 'modus operandi' of Truth supported by evidence and evolution.

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