Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

One equals Two


Date: 07/25/2001 at 17:36:12
From: Dick
Subject: One equals Two

There is an algebraic manipulation involving division by zero that 
results in one equals two, or some other contradiction. What is it?

This is a physics "proof" that one equals two.

Proof That One Equals Two

Beginning with the well known equations for uniform motion:
    s = 1/2(a)t^2
and solving each for acceleration, a :
    a = v/t and
    a = 2(s)/t^2
and setting them equal to each other:
    v/t = 2(s)/t^2
And using the fact that s = vt and substituting:
    v/t = 2(v/t)
Thus factoring each side by v/t:
    1 = 2
Ta Da!


Date: 07/25/2001 at 22:56:23
From: Doctor Peterson
Subject: Re: One equals Two

Hi, Dick.

We have a FAQ that gives several of these false proofs:

   False Proofs, Classic Fallacies
   http://mathforum.org/dr.math/faq/faq.false.proof.html   

You are probably aware that the main use of such fallacies is to teach 
us the dangers of unthinking manipulation of equations. That is just 
as important in physics as in math.

In your physics "proof," the problem is that you are using formulas 
that apply to different situations. The first two apply to the same 
falling body, at a fixed time t after being dropped (or exposed to a 
force), which results in velocity increasing from zero. But s = vt 
applies to a constant velocity, not a constant acceleration. And in 
fact, under constant acceleration, the average velocity happens to be 
just half of the instantaneous velocity, which accounts for the ratio 
of 1:2 you found.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Number Theory
High School Physics/Chemistry

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/