Puzzle Description:

There are 5 major mathematical constants; 0, 1, e (constant of exponential growth), pi, and i (square root of -1), and this true equation contains all 5 of them. Coincidence?

#1: Jan Young (haidapup) on Sep 30, 2008

perhaps not hmmmmmmmmmmmmm?

my head hurt real bad now...jk

My initial guess was Einstein's famous equation but I could not figure out why it would have the red coloration. A brain teaser within a puzzle to be sure. Thanks.

So if I read this equation correctly, it says, "'e' to the power of ['i' times 'pi,'] minus one, equals zero?"

So, please explain more. Why are these the only major constants in math? So the number "3," for example... if that isn't a constant, what else can "3" be?

Let me see if I understand. You are saying the number 3 could stand for the number 3 itself, or represent an exponent, or a cube root, etc, depending on where it's placed?

0 and 1 are numbers used in mathematical identities: a + 0 = a, a * 1 = a, a/b * b/a = 1, etc. While it's true that any number is technically a constant, 3 is no more particulary special than 4 or 5 or 29.

#3, the red is to make the puzzle solveable. In black and white, I couldn't solve it with logic alone. No hidden agendas, sorry.

Right. I just arbitrarily picked 3 as an example. Yes, it could have been any number.

I don't know why, but I was reminded of a joke a saw on another website:

"There are 10 types of people in the world, those who know binary and those who don't."

;-)

good puzzle, but the actual expression is e^(i*pi) PLUS 1 = 0, not MINUS 1.

Perhaps that will make it solvable in b/w??

EGAD!! What an embarrassing mistake! Thanks for the heads-up. The puzzle has now been fixed.

Re #4 (Adam): It's certainly true that 3 is a constant. So there are lots of constants in mathematics. The importance of 0 and 1 are pretty clear; 0 is the only number you can add to something and get that same thing back. Likewise 1 is the only thing you can multiply times something and get that thing back.

The others are very famous mathematical constants, probably the three most famous, because they come up in many situations.

Pi, you probably know, is the ratio of a circle's circumference to its diameter, approximately 3.1415926535897932384626433832795. It also appears in many other situations; for instance if you compute the sum 1/1 + 1/4 + 1/9 + 1/16 + ... + 1/n^2 for very large values of n, the result gets closer and closer to 1.644934066848226436472415166646, which is (Pi^2)/6.

i is defined to be the square root of -1. "But -1 doesn't have a square root", you cry, for there is no real number which you can multiply by itself and get a negative number. Well, that's true. But at times we wish there were, so we define i to be such a number, an "imaginary" number. It turns out that there are many real-world applications of imaginary numbers.

e is approximately 2.7182818284590452353602874713527. It is named for Leonhard Euler, the greatest mathematician of the 18th century, who noticed its many special properties. You can define it as 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + ..., or as the number that (1 + 1/n)^n gets close to as n gets large. If a large number of people put their names in a hat and then each draw a name at random, they will have to perform the experiment (on average) about e times before no one chooses his own name.

Now, it's not obvious what it means to take e to an imaginary power. But it turns out there's only one definition that makes any sense, and when you do that, the equation in the puzzle turns out to be true. And many people have noted how amazing it is that 5 important mathematical constants can be related so simply.

I could tell pretty swiftly it was going to be an equation, but I still couldn't help but think "42?"

Right? Douglas Adams all the way until i started solving

Perhaps "5 major identities"?

No, it's not coincidence.

Our mathematical constructs allow us to make sense of what exists. The ants in an anthill did not get out blueprints before they constructed the anthill; they constructed it according to instructions in their genes. We can interpret the shape of the little pile of sand in terms of the physics of gravity, and communicate that to other humans through mathematical language, but the anthill exists with or without our mathematical interpretation.

Well spoken, Bananas. I would point out, though, that math truth exists as well, notwithstanding the use of "imaginary," whether I understand it or not and whether I make use of it or not.

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