Connected Classrooms: How to Prove That 1 = 2 with Mathematician James Tanton

In this Connected Classrooms, students will learn del Monte's "proof," and many more, as Mr. Tanton tries to convince you that 1 and 2 really do equal each other! We'll use arithmetic and algebra, pure thought and physical experiments. Will you be able to find fault with any of his "proofs?"

About del Monte's "proof": Guidobaldo del Monte (1545-1647), a patron and friend of Galileo Galilei, believed he had witnessed the creation of something out of nothing when he established mathematically that 0 equals 1. Add one to both quantities and we get that 1 = 2.

*Suggested Ages*: Middle-High school students

*James Tanton* (PhD. Mathematics, Princeton University) is a research mathematician deeply interested in bridging the gap between the mathematics experienced by school students and the creative mathematics practiced and explored by mathematicians. He worked as a college professor for a decade, as a high-school teacher for a decade, and is now the Mathematician in Residence at the Mathematical Association of America in Washington D.C. 

James writes math books -- with publishers and through his own self-published means. He gives math talks and conducts math workshops all across the continent and overseas. He guides students and he guides teachers. He publishes articles and papers, creating and doing new math. And he shares the mathematical experience with teachers and students of all ages, helping them publish research results too!

[titasdutta]

In the algebraic proof,
x(x-1)=(x+1)(x-1) and then Mr. Tanton cancels out (x-1). But, it can't be done!
Because what he actually doing is dividing both sides by 0 as (x-1)=0 as x=1.
It is something messy...U cannot do that....because if u divide something by 0, U get something undefined or an is the fundamental problem..

[danielbarreto]

I don't understand how the fraction proof from 13 minutes is applicable universally. 

[delmar]

3691 over 9136 as a fraction does not equal 1 whole. According to the hack of just crossing out the 3's, 6's, and 9's, the aforementioned fraction leaves the 1 over 1. Even 369 over 936 is an exception as this fraction does not equal 0. As for the hand/arm trick, they key is turning the left counterclockwise. :) He talked of a mathematical truth...there is also a biological truth of an expecting mother equalling 1 whole mother = 1 whole mother plus the newborn baby: 1 = 2 ...or even 1 = 3 or more :)