The Beauty of Simplicity

Sometimes to approach something, one must try and think not only in the esoteric world of advanced mathematics but also in the simplistic world of basic abstract thinking.  Here’s a truly mesmerizing problem with an exceptional solution which I saw and just had to share.1226245517898095208.png

Hmmm… What to do, what to do.  Some very new things are brought up in this question, like how are you supposed to find the length when the string goes over the cylinder sideways?  At the same time you can sort of feel that something about this is gonna make it all make sense.   I strongly suggest you take some time (hours, days) to try it yourself before reading on.  Well I’m gonna jump right into the solution, which was pretty awesome.

Ok let’s imagine the cylinder was a paper tower roll.  What’ll happen if you cut a straight line down its entire length?  You can flatten it out so you have it’s entire surface area in the form of a rectangle, and let’s see what happens.

 

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Since we literally have the entire surface area out before us, the width is the circumference, 4 cm, and the length is still the same.  Remember that is all the string, because we essentially flattened out the whole surface area of the cylinder.  Each of the four sections of the string is just 5 right? That’s it?  The Pythagorean Theorem?  Are you kidding?  There are 4 sections, so the total length of the string is 20 cm.  Don’t know about you, but something about this problem sums up what I love in math.

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