Skip to main content

Proving that Pi Equals 3

...proves to be less of a pain than you might originally think. In fact, it's no problem at all to unravel millennia of careful mathematical postulation with just one simple trick. Can you spot it?

Given: a=b

(1) pi*a^2 = pi*a*b (multiplying pi*a)
(2) 3*a*b = 3*b^2 (multiplying by 3*b)
(3) pi*a^2 - 3*a*b = pi*a*b - 3*b^2 (subtracting (2) from (1))
(4) pi*a^2 - pi*a*b = 3*a*b - 3*b^2 (adding 3*a*b and subtracting pi*a*b on both sides)
(5) pi*a^2 - pi*a*b + a*b - b^2 = 4*a*b - 4*b^2 (adding a*b and subtracting b^2 on both sides)
(6) pi*a*(a-b) + b*(a-b) = 4b*(a-b) (factoring out common terms)
(7) pi*a + b = 4*b (removing common terms)
(8) pi*a = 3*b (subtracting b)
(9) pi*b = 3*b (substituting a for b since a = b)
(10) pi = 3 (removing common terms)

Therefore pi=3.

Spoiler ahead! If you want to figure it out yourself, then don't read on just yet!

The trick is actually the same employed over and over to prove all kinds of things in math, including that 1 = -1 and 1 = 2, among the more famous. Take a look at step 7. This is where the error is. In order to remove the terms, we must divide, right? Well, if a = b, then a - b = 0, thus we are dividing by zero, which is a big math no-no. Aside from being a fun trick to throw at your math students, it is a great example of why we can't divide by zero. Indeed, if we allowed it, then we can prove all kinds of false statements in our system!

Try your own hand at it for a minute. What other "convenient" conclusions can you come to? Can you prove that the world is like this math t-shirt? Maybe prove that e = 2 or that sqrt(2) = 1.5 or, if you're really adventurous, prove that pi = e!

Now, consider branching out into other illegal areas of math. :) How about negative square roots? What kind of false statements can you arrive at using that loop hole?

Just for fun, here is another fake proof. See if you can find the error:

(1) John = Time * Money (or anyone that you want to stick it to...)
(2) Time = Money (Time is Money)
(3) John = Money * Money (substitution)
(4) Evil = sqrt(Money) (Money is the Root of Evil)
(5) John = Evil

Of course, here the problem is in (4) because Paul said that the love of money was the root of all evil...har-de-har-har...oh, well, it was funny to me...

Comments

Popular posts from this blog

How Many Teeth Does The Tooth Fairy Pick Up Each Night in Utah?

Somebody asked me a question about my Tooth Fairy post the other day that got me thinking. How many baby teeth are lost every day in Utah?

I began with Googling. Surely someone else has thought of this and run some numbers, right? Lo, there is a tooth fairy site that claims that the Tooth Fairy collects 300,000 teeth per night.

That's a lot; however, when I ran the numbers, it started to seem awfully low.

Let's assume that the Tooth Fairy collects all baby teeth regardless of quality and we assume that all children lose all their baby teeth. The world population of children sits at 2.2 billion, with 74.2 million of them in the United States. Of those, approximately 896,961 of them are in Utah. This means that somewhere around .04077% of the world's children are in Utah.

If we assume that kids in Utah lose teeth at the same rate as all other children in the world and that each day in the year is just as likely as the rest to lose a tooth, then we have that of the alleged …

Five Reasons Serving on the Athlos Board is Fun Right Now

About 18 months ago, a friend of mine, Bethany Zeyer, let me know about an open position on the Athlos Academy of Utah school board. I've always had a passion for education, and my kids' school seemed like a place where I could have a positive effect on the community.

Also, I'd just finished reading "The Smartest Kids in the World" by Amanda Ripley and, based on Amanda's advice, interviewed the school's director.

I was in the mood to contribute!


I applied and was accepted, and I've been serving on the board for a little over a year now.

Since then, I've learned a whole lot about how a school is run.

I've learned that someone needs to determine the school guidelines for pesticide usage.



And that someone needs to be thinking about the long-term future of the school, whether or not to increase grade capacity, whether or not to match the pay increases big school districts are giving, and most importantly, evaluate whether or not the school is achi…

I don't know you from Adam OR How to Tie Yourself Back to Adam in 150 Easy Steps

Last Sunday, I was working on my genealogy on familysearch.org, a free site provided by The Church of Jesus Christ of Latter-Day Saints for doing pretty extensive family history. While looking for information about a Thomas Neal, I found an individual who had done a bunch of work on his family including is tie into the Garland family, which tied in through Thomas's wife.

So, while I was pondering what to do about Thomas Neal (who's parents I still haven't found), I clicked up the Garland line. It was pretty cool because it went really far back; it's always fun to see that there were real people who you are really related to back in the 14th century or what not.
As I worked my way back through the tree, I noticed it dead-ended at Sir Thomas Morieux, who, according to the chart, was the maternal grandfather-in-law of Humphy Garland (b. 1376).  The name sounded pretty official, so I thought I'd Google him. I learned from Wikipedia that Sir Thomas Morieux married Blanc…