Euclid’s The Elements: Preposition One-Really Fun Math Puzzle

This is the nth edition of *drum rolls* Pop Quizz! A quizz in which the answers are not obvious and if it is obvious, and you get it wrong, you are rebuked at!!!

Occasionally, I will occasionally ask a question, and the reader will answer them! For every wrong answer, I will consider one of your comments a spam. Ha! See how you like that suckers! (I am kidding, of course) Sometimes, a wrong answer won’t invite rage, some really obvious one will, and you will be called an idiot if you can’t answer the obvious one. In fact, I may have to make an extra page on my blog for the lists of idiots. :)

Anyways, once upon a short time ago, I was reading Euclid’s The Elements, which is basically the geometry book to rule them all. First, it defines various terms, and go over postulates. Then it goes through geometric proofs, each different one called prepostitions. Well, the first one I think is a really neat geometry problem. It goes like this:

3. On a given straight line to construct an equilateral triangle.

Meaning, considering you have a line AB, make a triangle ABC with all sides equal. Sounds hard? Well, if you hear the clue, you migh go “OOOOHHHhhhhh!” If not, well… shame on you, mate. ^_^














Clue: Use two circles with the same size, call one circle A, call the other one B, then you will see. I swear, if I give you more, it will be a dead give away.


And the answer is…



*drum rolls*










*dying with anticipation*










Create a circle with center A of the line and another circle with center B of the line. Make their radius equal to the lenght of the circle. You will notice it will look like the venn diagram. Well, guess what, the line in the thickest part of the intersected area, line AB is equal to the radius of both circles! Now, see that there are two parts in which the circumference of the circles intersect, right? Name one of them point C. Now, connect point A and point B and connect it with C, and you have a triangle.

Well… you have triangle, so I guess this is over, right? Not so fast! We have to PROVE whether the triangle is equilateral. That is the imaginary contract that you have agreed to, signed, and then thrown away down your memory hole. So, what to do next, what to do next… That, my friend, is something for you to figure it out for yourself. Don’t worry, I will post an update, but in the mean time, look at this diagram I made for a zillion years ’til you are able to figure it out. If you don’t… Maybe you need to do something else with that feeble mind of yours. (You know that I am kidding, I will do anything to increase your passion at mathematics ^_^)


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