Transcendental Numbers

• Infinity, Pi, and Stranger Things [Robert, 7/15/1996]
  Imagine there's an infinite string attached to the top of your head, and you're dangling from it... somewhere along your spine, you have an itch you can't scratch...

• The Number e [Wong, 6/3/1996]
  Is "e" a number like Pi? How does "e" relate to continued fractions?

• Numbers [Greeno, 12/10/1997]
  How do integers and whole numbers, rational numbers, transcendental numbers, and counting numbers relate to each other?

• Why is "e" so important? [Chang, 1/8/1995]
  Why is "e" so important? How significant is "e" compared with "pi?" How did it come about? How is it defined? Why is it taught only at higher level mathematics? Are there other numbers like "e"?

• Transcendental numbers [Young, 11/17/1994]
  We just learned about e today and how it is similar to pi because it is irrational without a radical. Are there any other transcendental numbers, and if so, how are they used?

• Are Transcendentals Irrational? [Counides, 9/2/1995]
  Are transcendental numbers a subset of the irrationals?

• Proving a Number is Transcendental [Sutorius, 4/12/1996]
  How does one prove a number is transcendental?

• e - The Transcendental Number [baure, 5/16/1996]
  Can you help us find a history of "e", the transcendental number?

• Transcendental Numbers [Lewis, 5/31/1996]
  a=.110001000000000000000001..... Where is the next 1?

• Euler Formula: e^(pi*i) = -1 [Lucas W Tolbert, 6/5/1996]
  Why does e^(pi*i) = -1?

• Doesn't Pi Ever Repeat? [Zipshark, 7/8/1996]
  How do people know that pi goes on forever without repeating?

• e^x Appreciation [Danzig, 7/9/1996]
  What is the history of e^x? What do you think of it?

• Irrational Pi [Newton, 7/15/1996]
  Why is pi considered an irrational number when it's defined as the ratio of the circumference of a circle to its diameter?

• What is e? A Ratio? [Bobkane, 7/25/1996]
  Pi is the ratio of the circumference of a circle to its diameter. Is there a similar explanation for e?

• The Reality of e [Kane, 7/26/1996]
  Does e exist outside of the classroom? Can I find it in nature?

• e^(pi*i) = -1: A Contradiction? [Rwitte, 8/17/1996]
  I know that e^(i*Pi) = -1. But squaring and taking a natural log of both sides, you get 2*i*Pi = 0. Please explain.

• Euler Equation [Davis, 01/21/1997]
  What is the meaning behind e^(pi*i) = -1?

• The Nature of e [Chen, 02/23/1997]
  Why is e considered natural?

• Intriguing Limit [Oliver, 04/30/1997]
  Why is the following true: lim x --> oo (1-1/x)^x = 1/e?

• Gregory's Series [Jim, 06/14/1997]
  Where does this series 4[1 - 1/3 + 1/5 - 1/7 + ....] for pi come from?

• How Pi is Calculated [Krono, 08/07/1997]
  If pi is calculated by dividing the circumference of a circle by its radius, how can computers generate pi to billions of decimal places?

• Numbers that represent pi [Ferrer, 08/08/1997]
  If pi is an inexact and transcendental number, how in the world did we obtain a certain series of numbers to represent pi?

• e^(i*pi) = -1: pi = 0 ? [Koehler, 10/17/1997]
  I have been playing with the equation e^(i*pi) = -1 and have found some disturbing things...

• The Limit of (1+1/x)^x As x Approaches Infinity [Harvey, 02/17/1998]
  How Euler calculated e, and what it has to do with the equation (1+1/x)^x.

• History and Applications of the Natural Logarithm [Fornwalt, 03/02/1998]
  I'm so surprised at how often the number e comes up. Where did it come from? Who first derived it? Why is it so common in the field of biology?

• Alabama legislature and pi [Dell, 04/15/1998]
  Did Alabama really vote that pi should have its biblical value of 3?

• The Irrationality of e [Brady, 09/04/1998]
  Are there any simple proofs to show that a number like e is transcendental? What about irrational?

• Facts about e [Clarissa, 11/09/1998]
  Where does the number "e" come from and what uses does it have in the real world?

• Compounding Interest and e [Radway, 11/11/1998]
  How is the number e derived from compounding interest? Does it come from the series expansion of e?

• Natural Logarithms [Harvey, 11/23/1998]
  Why are logarithms to the base e called "natural"?

• Proving Pi is Irrational [Sandler, 01/06/1999]
  How do you know that pi never repeats? How would you show that it is irrational?

• Pi and Polygons [Eric, 03/14/1999]
  Derive a formula to find the angle of an n-sided polygon with x sides.

• "Accidental Order" in Pi, e [Ngeno, 04/12/1999]
  Using a result of Dirichlet's to prove that a given sequence will appear in infinitely many prime numbers.

• Proving Transcendence [Johnson, 05/15/1999]
  How does one prove transcendence in a number?

• How Can Pi Not Repeat? [Chan, 06/01/1999]
  Won't pi repeat when it runs out of number combinations?

• Proof that e^i(pi) = -1 [White, 06/02/1999]
  How can it be proven that e^[i(pi)] = -1? And why does it matter?

• Find the Flaw [Dan, 08/02/2001]
  I don't understand where the following proof goes wrong...

• Complex Powers [Bill, 09/28/2001]
  How do I show that abs(z^i) is less than exp^pi where z is a complex number not equal to 0?

• Proofs of e [Christine, 03/21/2002]
  I found out that the definition of e is: e = lim, as n approaches infinity (1+1/n)^n. Is there a proof for this or for 1+2(e-1/n)?

• e^pi vs. pi^e [Rajesh, 03/20/2002]
  Which is greater, e^pi or pi^e? I would like to have a simple proof.