Charles Hermite and transcendental numbers

OLYMPUS DIGITAL CAMERA
OLYMPUS DIGITAL CAMERA

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.

920mini-08

http://mrburkemath.blogspot.co.uk/2014/10/x-why-mini-algebra-problems.html

Reggeo1601-21.png

 

http://www.britannica.com/biography/Charles-Hermite

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.

http://www.mathsisfun.com/numbers/transcendental-numbers.html

{ 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

maxresdefault.jpg

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
Yet
“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: http://www.historytoday.com/patricia-rothman/william-jones-and-his-circle-man-who-invented-pi#sthash.4bbJtftH.dpuf

2012-05-12 10.31.12-44

 

 

http://www.historytoday.com/patricia-rothman/william-jones-and-his-circle-man-who-invented-pi

https://www.exploratorium.edu/pi/history_of_pi/

 

http://mrburkemath.blogspot.co.uk/2014/10/x-why-mini-algebra-problems.html

This is meant to be humorous

Stan,Emile and the bath

    • Stan was leaning over, cleaning the new bath.When the doorbell rang,he rushed downstairs and opened the double front door.
      “Will you take this parcel in for the lady next door?” The postman asked wearily.
      “Oh,fine Stan stuttered.He was trying to avoid Annie but here she was,coming down the road of superior semi detached houses suitable for ex-headmasters ,small businessmen,econometricians,surgeons,pie salesmen and theologians.

      She was wearing perfume, and green sandals from TK Maxx,light khaki tencel cropped combat trousers with a purple silky over-blouse, not to mention her matching raspberry and cream underwear .Round her neck hung a miniature grandfather clock on a solid gold chain,and she had three imitation gold and silver watches on each of her three wrists making a total of 333 watches according to Carnap’s theory of logic and Russell’s terrible handwriting.

      Stanley didn’t know that she had a mobile phone stuffed into her bra—one advantage for the larger sized woman.In fact she had 4 down there in her raspberry coloured glamour bra,as she had a phobia about their batteries running down all at once
      The more she had the lower the probability of her being without a phone whilst out and about the town and countryside.
      So she reasoned in her womanly way. J
      ust then one phone rang.She rummaged around to the consternation and turmoil-uation of Stanley and the postman.She plucked out a pale blue phone.
      “Hi,it’s Annie” she murmured.
      “Hi Annie it’s Dave the paramedic with carpentry skills. You’ve not rung 999 lately so we were wondering if all was well!”
      “Oh,I’m terribly sorry.I’ll try to phone later on.Thanks,Petal.
      That was Dave,our ex-transvestite converted paramedic”,she informed the men.The postman galloped off on his donkey, his bags full of undelivered males.
      It’s a tough but interesting life in Knittingham. Would you like a male delivery?Contact Parcel Force without delay.
      Annie went into Stan’s house and demanded a cup of coffee.
      “Won’t it make you put weight on” Stan quipped ironically.
      “Do you think I’m too plump?” she responded anxiously..
      “Too plump for what?” he quipped amiably.
      “To attract men,of course!”
      “No,my angel,you are just perfect”he quacked definitively.”Nor are you an angel,strictly speaking,as I have good reason to know.Thank you,my beloved for love rendered so generously .”
      “Oh,my goodness I must get home to render the fat from the beef and to make some gooseberry jam.”
      Stanley looked uneasy.
      “I wonder why babies are left under gooseberry bushes?
      The thorns are so big it’s quite dangerous getting them out,or so Mary told me when Lyra was born. She was covered in scratches and wouldn’t come near me for months.”
      “Why don’t you come upstairs to look at our new purple bathroom suite.Since the Royal Wedding it’s the in colour.The gold taps were expensive but they do go well.”
      “My God,let me out.” she bawled,”It reminds me of the Vatican and that’s no place for a lady”,
      “Not even a gay lady?” Stan muttered parsimoniously, as he licked her eyelashes gently.
      “Stop that.I’ve got my Yves St Laurent mascara on.”
      “I prefer the taste of the Chanel,”he disclosed privately in an internal secret memo.[available on 50 years]
      “Why not lick my neck instead?” she enquired curiously as she tripped over Emile the cat, who had slipped into the bathroom as usual to see what they were up to,you know what I mean, you catch my drift?
      She fell floppily into the bath and banged her head on the taps.
      “Oh,gosh,better ring 999” Stan said to Emile.
      “Have you got your catphone warehouse mobile on you?”
      “Yes ,it’s in my y-fronts”, the cat amiably miaowed.
      “Hi Dave,this is Emile.Can you come quick.Annie is unconscious and what is worse,she has scratched the new bath.”
      In fact it was Emile who had scratched the bath that morning but since Stan had not noticed he hoped to, callously, pass the blame onto poor Annie.
      How cruel can a cat be? Ask any mouse! Still in the end God made all of us and what a terrifying and beautiful world it is.
      And of so say all of us

%d bloggers like this: