Charles Hermite and transcendental numbers


The story of numbers is enough to make one believe in a Higher Power or even a transcendental Power?

A Concise History of Mathematics [Fourth Revised Edition] Paperback – 1 Nov 1987

 This topic  will take your mind off Brexit and help you regain a sense of awe and wonder.This cartoon has an equation on it.But some numbers are never found as the answer to such an equation.And that can be proved.And some of the proofs are quite easy.



Hermite  might not have succeeded nowadays as passing exams was not easy for him.I suspect he was a person who preferred to  spend his time  on his own  interests in Mathematics and to neglect his wider studies

I have referred in some of   my  Stan  stories to the number “e”.Hermite was the first to prove  that e is not an algebraic number.

{ see the article].

It may surprise many people that there are different kinds of numbers  ,beginning with the integers 1.2.3…… and the rational numbers  [fractions like 1/2 4/5   89/54 etc.]
The Babylonians discovered  the  ratio of the circumference of a circle to its diameter was fixed regardless of the size of the circle.We call it pi.It is not an integer nor a raional number.The number of integers is infinite.

“The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. One Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for pi, which is a closer approximation.” [from link below]

They used 3 as an approximation and  in the Hebrew Bible 400 BCE the Temple was  made using 3 as an approximation. Archimedes got closer.But.   like e, pi cannot be expressed as a fraction.
Some other numbers like the square root of 2 are irrational  [ that is,not fractions[ but they are algebraic.As in x squared =2

Relating to Solomon’s temple.They used pi =3.It is in the  Hebrew Bible


Real numbers are all numbers from integers to the transcendental and they are uncountably infinite
Pi and e are called transcendental numbers.We don’t know many other
“The set of transcendental numbers is uncountably infinite. Since the polynomials with rational coefficients are countable, and since each such polynomial has a finite number ofzeroes, the algebraic numbers must also be countable. However, Cantor’s diagonal argument proves that the real numbers (and therefore also the complex numbers) are uncountable. Since the real numbers are the union of algebraic and transcendental numbers, they cannot both be countable. This makes the transcendental numbers  uncountably infinfte

Quote from article below {Euler is usually credited with this]

:In 1706 a little-known mathematics teacher named William Jones first used a symbol to represent the platonic concept of pi, an ideal that in numerical terms can be approached, but never reached.

William Jones, mathematician from Wales, 1740

William Jones, mathematician from Wales, 1740

The history of the constant ratio of the circumference to the diameter of any circle is as old as man’s desire to measure; whereas the symbol for this ratio known today as π (pi) dates from the early 18th century. Before this the ratio had been awkwardly referred to in medieval Latin as: quantitas in quam cum multiflicetur diameter, proveniet circumferencia (the quantity which, when the diameter is multiplied by it, yields the circumference).

– See more at:

2012-05-12 10.31.12-44

This is meant to be humorous

I welcome comments and criticism

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