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# 409

April Fools Math - April 1, 2011
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Thanks to those who participated in the Facebook poll regarding "What is your biggest mathematical surprise?". I decided to go with the most popular option for this comic :P

Nice one.

Hahahha great post, I always liked how maths can fool some of our most basic presumptions.

By the way, I suppose the question about the derivate is some type of anti-robot question. but, for me, is answered already, Firefox knows how to derivate?

Yup, Firefox knows all.

I actually use javascript to fill in the answer. The question is only meant to prevent spam (I was originally getting 20-40 spam posts per day before it, and now I get 0-3 per day).

1. The question is always for 2x
2. But what about people who don't know calculus
3. Its filled for me too on chrome
4. But the spikedmath registering was not
5. But if its already filled, how does it prevent spam?

Nice one.BTW why is the guy labeled 47?

i have a suspicion it is a reference to Euclid's Elements...

It's a geek reference (to Star Trek:TNG and possibly elsewhere). It's amusing that the non-geeky character in this comic is the one wearing it as a number on a sports jersey.

Nice! I think I had the same reaction the 1st time a teacher started introducing non-Euclidean geometry to me.

you yelled april fools?

One thing I find most interesting about such triangles: the sum of the angles will tell you how much of the area of the sphere they cover. Using radians, the triangle's angular excess (over π) will be up to nearly 2π, and gives the area, vs. the sphere's area of 4π. This three-right-angle one has an excess of π/2, and covers (π/2) / 4π = 1/8 the sphere.

Correct. Note that we could also view the "exterior" of the depicted triangle. That has three angles of 270 degrees (3Pi/2 radians) each, an angular excess of 7Pi/2, and covers seven eights of the Earth's surface.

Agree with Chas. The triangle should reach the equator in Northern Brazil and the zero meridian thru London to match with the text. Most likely Mike had no suitable projection/map at hand that would show all the three vertices (and possibly also most of North America?).

Yup, you're both right. I thought about the accuracy and figured it wasn't worth the extra minutes/hours to be that technical :P

If the equatorial vertices are moved further apart, the polar angle increases up to almost 2π. Similarly, if the eastern point is moved south through the south pole and continues circling onwards towards the north pole, the western angle increases up to almost 2π. In either case the shape is almost a spherical cone and the angles sum to 2π + π/2 + π/2 = 3π.

However, if all the points are dragged backwards until they almost meet on the opposite side of the earth (so the triangle covers almost the whole earth) the angles would each be 2π/3, summing to just 2π.

What's the largest sum of angles, and what would the shape be?

The geography isn't quite as good as the math -- those locations on the globe aren't anywhere near the pole or the equator. Labeling the top vertex A, the left B, and the right C, I estimate A=80N,20W; B=24N,100W; C=15N,17W. These values mean the arcs (in degrees) are a=77.7, b=65.01, c=64.65, and the angles are A=87.75, B=67.97, C=67.55, for a total of only some 223 degrees.

But I suppose this is over-analyzing.

[Comment removed by moderator (usually I catch the spam before you see it :P); Mike]

^SPAM!!!

Lets go non-Euclidean on this spammer!

Exile her to the outside of a triangle approaching the 4π excess limit.

Spiked Math, I love your comics!!! I've read every single one of them and I always look forward to new ones:) This one made me LOL!

I may not be a mathematician, but as soon as we transform the triangle in order to be contained in a sphere surface, I wouldn't call it a triangle. Blame me and my semi-idiocy. :P

Nice one!!

Actually, the teacher has a point. It is impossible on a plane (Euclidean) yet might be possible on a non-Euclidean space.

Welcome to Spiked Math!

Hello my fellow math geeks. My name is Mike and I am the creator of Spiked Math Comics, a math comic dedicated to humor, educate and entertain the geek in you. Beware though, there might be some math involved :D

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