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Not everyone understands that mathematics can be beautiful. Sometimes we get too mired down in the nuts and bolts to get to the beauty. But here’s a problem from Brilliant.org that is pretty to look at, and the solution is beautiful, as well as astonishing, I think.

The ability to be astonished is something I’m working on this year–to appreciate the beauty in God’s creation or in a well-functioning organization or in the kindness of people. I don’t want to take life for granted. I’ll write more about that later.

So here’s a beautiful problem, just in its appearance.

The question is, what is the total area in orange? There is a formula for the area when circles overlap. It’s medium complicated, and in this case, even with all seven circles of radius 1, pi is involved, as well as the square root of 3. But the answer, surprisingly (astonishingly!), is 2 pi. So the picture is aesthetically pleasing, and the answer is too.

There is beauty everywhere, and we are encouraged to find it:

Finally, brothers and sisters, whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable—if anything is excellent or praiseworthy—think about such things.

(Philippians 4.8, NIV)