Mathematics
This presentation is the property of its rightful owner.
Sponsored Links
1 / 16

Powerpoint Templates PowerPoint PPT Presentation


  • 48 Views
  • Uploaded on
  • Presentation posted in: General

Mathematics Non-euclidian Maths. Powerpoint Templates. Once upon a time Euclid had 5 axioms It shall be possible to draw a straight line joining any 2 points. A finite straight line may be extended without limit in either direction.

Download Presentation

Powerpoint Templates

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Powerpoint templates

Mathematics

Non-euclidian Maths

Powerpoint Templates


Powerpoint templates

  • Once upon a time Euclid had

  • 5 axioms

  • It shall be possible to draw a straight line joining any 2 points.

  • A finite straight line may be extended without limit in either direction.

  • It shall be possible to draw a circle with a given centre and through a given point.

  • All right angles are equal to one another.

  • There is just one straight line through a given point which is parrallel to a given line.


Powerpoint templates

But then along came Riemann and his Contraries

  • Two points may determine more than one line (axiom 1)

  • All lines are finite in length but endless

  • (axiom 2)

  • There are no parallel lines

  • (axiom 5)

a. All perpendiculars to a straight line meet at one point.

b. Two straight lines enclose an area.

c. The sum of the angles of any triangle is greater than 180 degrees.


Powerpoint templates

Georg Friedrich Bernard Riemann (1822-66)


Powerpoint templates

But then along came Riemann and his Contraries


Powerpoint templates

Albert agrees…space is curved


Powerpoint templates

Riemann

  • Two points may determine more than one line (axiom 1)


Powerpoint templates

Riemann

  • All lines are finite in length but enless (axiom 2)


Powerpoint templates

Riemann

  • There are no parallel lines

  • (axiom 5)


Powerpoint templates

M.C. Escher


Powerpoint templates

M.C. Escher


Powerpoint templates

Riemann vs Euclid

Neither have even been proven wrong, and yet they contradict each other???

Systems work within their own axiom sets

Godel (1906-78), Austrian


Powerpoint templates

Kurt Godel (1906-78) – Incompleteness Theorm

It is impossible to prove that any mathematical system is free from contradiction

He didn’t prove that Maths has contraditions, just that it’s impossible to prove it doesn’t


Powerpoint templates

Kurt Godel – Incompleteness Theorm

However,

Maths hasn’t had any contraditions since it’s formalisation 2500 yrs ago – so most mathematicians mostly ignore Godel’s theorm


Powerpoint templates

So if Riemann, Godel & Einstien have contradicted Euclidian maths, why do we still use it?

Because it works!

Why does it work?


  • Login