“Math, Revealed,” our four-part series exploring the mathematics behind everyday objects and experiences, recently came to a smashing conclusion. One installment took a spin through “taxicab geometry,” a wacky but vital corner of mathematics in which circles aren’t round and pi equals 4. Another journey began with apples and pentagrams and led to Leonardo da Vinci, the golden ratio and ideal positioning of belly buttons.
We had great fun on this adventure and hope to resume it before too long. In the meantime, here’s a quiz to test what you learned and your general math knowledge. Enjoy!
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Jens Mortensen for The New York Times 
Jens Mortensen for The New York Times 
Jens Mortensen for The New York Times 
Jens Mortensen for The New York Times 
Jens Mortensen for The New York Times 
Jens Mortensen for The New York Times 
The New York Times, photo via Alamy 
Photo illustration by The New York Times, source photos by Balarama Heller for The New York Times
1. In taxicab geometry, circles don’t look round — they form sharp, angular shapes. What shape do they resemble?
2. In taxicab geometry, even the value of pi is a surprise. What is it?
3. Mathematicians have long been fascinated by a special number that describes self-similar proportions. What is the approximate value of this “golden ratio”?
4. Leonardo da Vinci’s “Vitruvian Man” has been analyzed endlessly for hidden patterns. According to a 2015 study, does the navel divide the figure according to the golden ratio?
5. In the densest possible arrangement of soda cans standing on a flat surface, each can in the middle touches the same number of neighbors. How many is it?
6. In 2022, a mathematician won a Fields Medal for solving a problem about how to pack spheres tightly in eight dimensions. Who did it?
7. The first four triangular numbers are 1, 3, 6 and 10. Why is 10 considered a triangular number?
8. In 1672, Gottfried Wilhelm Leibniz found a clever way to add the reciprocals of all the triangular numbers. What sum did he get? 1 + 1/3 + 1/6 + 1/10 + …
9. At a wedding reception, the bride seats eight of her ex-boyfriends together at a table. (This actually happened to me once.) If each ex-boyfriend shakes hands with each of the others, how many handshakes occur in total?
10. Four bugs start in the corners of a square that measures 1 foot by 1 foot. Each bug chases its clockwise neighbor, always crawling directly toward the neighbor’s current position. If they all crawl at the same speed, how far does each bug travel before they all meet at the center?
Questions and answers 1 through 8: photo illustrations by Jens Mortensen for The New York Times; answer 6: photo by Brendan Hoffman for The New York Times; question 9: photo illustration by The New York Times, source photo via Alamy; question 10: photo illustration by The New York Times, source photos by Balarama Heller for The New York Times.
Produced by Alan Burdick, Alice Fang, Marcelle Hopkins and Matt McCann.