The perfection of the pythagoras scale of numbers

Alternative Numbers Pythagorean Numerology Pythagoras was an ancient philosopher also known as "the father of numbers". The theory that numbers are attractive to themselves was defined by Pythagoras already in the sixth century B. Father of geometry, teacher of astronomy and founder of the diatonic scale laws of musical progression by which we still tune our pianos today Pythagorean numerology assigns numbers non-numerical traits.

Pythagorean Triples and Perfect Numbers One of the rather frequent quotes touching on the nature of mathematics is due to the famous Bertrand Russell: Outside of the profession, the quote is mostly misunderstood to be derogatory of mathematics.

In an online pollthis is the second least picked out characterization of mathematics. But, as John Paulos has observed in his influential book, Beyond Numeracythe quote does give a succinct, albeit overstated, summary of the formal axiomatic approach to mathematics. Indeed much of mathematics consists of implications that deal with objects of an entirely abstract nature.

Even the simplest of the mathematical objects, say natural numbers, are abstract entities that one does not meet in a real world. Ron Aharoni in his recent Arithmetic for Parents suggests a surprise request in a first lesson on denominations: A rich history of perfect numbers has been recently supplemented by an implication of the sort that B.

Pythagorean Scale

Russell had in mind. The number c is called the hypotenuse of the Pythagorean triple. Prove that an even perfect number cannot be the hypotenuse of a Pythagorean triple. Prove that if there is an odd perfect number, then it is the hypotenuse of a Pythagorean triple.

A natural number is perfect if it is equal to the sum of all its divisors excluding itself. Observe the second part of the problem. While the even perfect numbers have been an object of study from the time of Euclid, no odd perfect number has ever been found.

No one was able to prove that they do not exist either; there are none below and although there are serious doubts there are any beyond this bound, a group of enthusiastic devotees is currently working on raising it to The problem is in the spirit of many results concerning odd perfect numbers, the first of which is probably due to Freniclesee [ Dicksonp.

But to return to the problem, an even perfect number n must be of the form 2k-1 2k - 1 with 2k - 1 prime. This answers part a of the problem. By a result of Fermat [ Hardyp.Pythagoras and the Mystery of Numbers. by.

Kate Hobgood. Pythagoras Pythagoras was the first of the great teachers of ancient Greece. Born in B.C., Pythagoras became one of the most well known philosopher and mathematician in history. Creating the Pythagorean Brotherhood, his teachings greatly influenced Socrates, Plato, and Aristotle.

It is said that the Greek philosopher and religious teacher Pythagoras (c. BC) created a seven-tone scale from a series of consecutive perfect fifths. The Pythagorean cult's preference for proportions involving whole numbers is evident in this scale's construction, as all of its tones may be derived from interval frequency ratios based on the first three counting numbers.

In addition we strongly recommend to peruse the lively and very informative discussion on the history of Pythagoras on the Sound Healing Forum, which Delamora Transformational Experiences is a member regardbouddhiste.comon: Brookline Court Naperville, IL, United States.

It is said[4][5][6] that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of (perfect fourth), (perfect fifth), (octave), forming the basic intervals of the Pythagorean scales.

numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes.

For example, the number one was the generator of all numbers; two represented opinion; three, harmony; four, justice; five, marriage; six, creation; seven, the seven planets or “wandering stars”; etc.

Odd numbers were thought of as female and even numbers as male.