Category Archives: Geometry

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 | Leave a comment

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 | 2 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 | 12 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 | 7 Comments

Q: If Earth was flat, would there be a horizon? If so, what would it look like? If the Earth was flat and had infinite area, would that change the answer?

Physicist: There’d definitely still be a horizon if the Earth were flat.  It would be in almost exactly the same place, and look essentially identical.  While the Earth isn’t flat, adherents to that theory are correct in that it’s nearly … Continue reading

Posted in -- By the Physicist, Geometry, Physics | 26 Comments

Q: How would the universe be different if π = 3?

Physicist: We sometimes get questions about physical constants changing, and those questions make sense because there’s no real reason for the constants to be what they are.  But π is mathematically derivable; it kinda needs to be what it is.  You … Continue reading

Posted in -- By the Mathematician, -- By the Physicist, Geometry, Math, Philosophical, Physics | 22 Comments