Category Archives: Geometry

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 | 25 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

Q: How are fractals made?

Physicist: There are a lot of ways. A fractal is just a structure that stays interesting no matter how far you zoom in.  More than that, generally you can’t tell how far you’ve zoomed in (it looks the same at … Continue reading

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

Q: Why does light choose the “path of least time”?

Physicist: Light travels at different speeds in different materials.  When you shine a beam of light from one material into another (like from air to water) it bends in such a way that the path it takes from one point … Continue reading

Posted in -- By the Physicist, Equations, Geometry, Logic, Physics | 10 Comments