Question

How do you prove a number, like e or pi, to be transcendental?

Asked by: Nathan Douglass

Answer

There is no general theorem that identifies transcendental numbers to my knowledge. However, there are theorems that do so for special cases. Of these theorems, Gelfond's theorem is probably the most useful. It states: If a number 'r' is not the root of any polynomial equation with integer coefficients of any degree, then 'r' is transcendental.

Cantor proved the existence of transcendental numbers. Hermite (1873) proved that the number 'e' is transcendental. Lindemann (1882)proved that 'pi' is transcendental.

Answered by: Vince Calder, Ph.D., Physical Chemist, retired


Answer

You can find a fantastic explanation of transcendental numbers, and their history at the following website: http://mathworld.wolfram.com/TranscendentalNumber.html

Answered by: Eric Baicy, B.S., Seattle

Search

Loading



Sponsors

USC University of Southern California Dornsife College Physics and Astronomy Department McMaster University Physics and Astronomy Department

Science Quote

'You cannot hope to build a better world without improving the individuals. To that end each of us must work for his own improvement, and at the same time share a general responsibility for all humanity, our particular duty being to aid those to whom we think we can be most useful.'

Marie Curie
(1867-1934)

Deal of the Day

Image of Shark Tooth Fossil in Matrix. Click on this image for more info. Shark Tooth Fossil in Matrix
Regular Price: $39.95
Today's Price: $15.00
Superb shark fossil specimen for the science classroom! Buy it now! Deal ends at midnight!

Top Selling

Here are our physics & astronomy bestsellers:
Mini Plasma Ball
Slide Making Kit
Top Secret - Spinning Top
Wood Grain Newtons Cradle
Deluxe 3D Mirascope
Solar Radiometer
Periscope
Solar Science 4M Kit
Ultimate Chemistry Set CHEM C3000
3D Magnetic Field Tube