Category Archives: Geometry

Q: Is π the same in every universe?

Mathematician: That depends on what you mean by “universe.”  Here’s a framing: A circle of radius R centered at a point P is the set of all points in the plane with distance R from P.  The diameter D of … Continue reading

Posted in -- By the Mathematician, -- By the Physicist, Geometry, Math, Philosophical | 27 Comments

Q: How was the number π first discovered? How did we first figure out it was 3.14…?

Physicist: Unfortunately, the use of the number π is older than recorded history so… who knows?  But the use of π at the beginning of recorded history wasn’t too sophisticated, so we can make guesses. π is the ratio of … Continue reading

Posted in -- By the Physicist, Engineering, Geometry, Math | 10 Comments

Q: Given two points on the globe, how do you figure out the direction and distance to each other?

Physicist: The very short answer is: use the spherical law of cosines so you can do trigonometry on a sphere. This is a seriously old problem that needed to be solved before we became a routinely globe-trotting species.  If you … Continue reading

Posted in -- By the Physicist, Geometry, Math | 9 Comments

Q: Is it possible to eat all of the ice cream in a bowl?

Physicist: If you’ve ever sat next to someone as they rang an almost-empty ice cream bowl like church bells on Sunday, then you’ve probably asked yourself some variation of this question. Clearly, the issue is that a spoon and a … Continue reading

Posted in -- By the Physicist, Geometry, Philosophical | 11 Comments

Q: What determines the size of the bright spot when you focus sunlight with a lens?

Physicist: This question really appeals to my ten-year-old self.  If you’ve never tried to burn something with a lens, collect three pairs of sunglasses, a magnifying lens, and something you dislike.  On a bright day, put on all three pairs … Continue reading

Posted in -- By the Physicist, Equations, Geometry, Math, Physics | 1 Comment

Q: Can planes (sheets) be tied in knots in higher dimensions the way lines (strings) can be tied in knots in 3 dimensions?

Physicist: Yes! Mathematicians are pretty good at talking about things in spaces with any number of dimensions.  Sometimes that math is fairly easy and even intuitive.  For example, a line has 2 sides (ends), a square has 4 sides, a … Continue reading

Posted in -- By the Physicist, Geometry, Math | 10 Comments