Category Archives: Geometry

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 | 8 Comments

Q: How do I know my windmill is on straight?

The original question was: I got quite the challenge from my father in law. The problem is well defined, but I’m having difficulties finding a meaningful answer. The reason why he asked me is because I’m an engineering student and … Continue reading

Posted in -- By the Physicist, Engineering, Equations, Geometry, Math | 4 Comments

Q: Why radians?

Physicist: Because calculus. When you first start doing trigonometry the choice between radians, degrees, turns, or hexacontades is a matter of personal preference.  Most people use degrees because most other people use degrees (and other people seem pretty on the … Continue reading

Posted in -- By the Physicist, Conventions, Geometry, Math | 7 Comments

Q: Why is the area of a circle equal to πR2?

Physicist: To demonstrate this you typically have to use either calculus or oranges.  They both use more or less the same ideas, they’re just applied in different ways. Oranges: Imagine taking an orange wedge and opening it so that the … Continue reading

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

Q: How do we know that π never repeats? If we find enough digits, isn’t it possible that it will eventually start repeating?

Physicist: In physical sciences we catalog information gained through observation (“what’s that?”), then a model is created (“I bet it works like this!”), and then we try to disprove that model by using experiments (“if we’re right, then we should … Continue reading

Posted in -- By the Physicist, Geometry, Logic, Math | 21 Comments

Q: How do you prove that the spacetime interval is always the same?

The original question was: Here’s my current dilemma: how does one rigorously prove the invariance of the space-time interval?  In Taylor & Wheeler’s Spacetime Physics, they basically show one very good example of the invariance, then they instruct the reader … Continue reading

Posted in -- By the Physicist, Geometry, Math, Relativity | 15 Comments