I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series...
While chess hasn't been solved yet, other games have. For example, I know that in in some games, like connect four, if both players play perfectly, the player who goes first will always win. On the other hand, some games, like tic tac toe, a perfect game will result in a draw; in fact, I...
Recently I started looking back at some basic mathematical principles, and I started thinking about the theorem of corresponding angles. It's such a basic idea that it seems obvious on an intuitive level, but despite that (or possibly because of that) I can't think of a good way to formally...
Quick update: I decided to extend the chart that only graphs the vertices of the parabolas to include the vertices from equations using equations with angles between 0 and 180 degrees instead of just up to 90 degrees, and this is the result:
It looks like an ellipse. Does anyone know why it...
Thanks a bunch! I didn’t know that was called an envelope before so it’s really nice to have a name for that kind of thing, and the Wikipedia page looks pretty interesting. Still, from what I can tell, it seems like the second chart, derived from only plotting the vertices of the various...
Recently I was playing around with the idea of graphs of projectile motion and I started wondering what it would look like if someone were to graph every parabolic trajectory of a single initial velocity over all angles between o and 90 degrees above the horizontal. I decided to find out so in...
Darn, that's too bad. Still, I figured that there was a decent possibility of that being the case going in. Still, even if there are no concrete answers, do you know if there are any common of popular hypotheses going around the scientific community on the subject? In any case, thanks for the...
In physics, at least at my level of knowledge and understanding, a lot of the most basic facts of reality start to seem a bit arbitrary. Mostly this seems to be the case with the various universal constants such as the speed of light or plank's length or the gravitational constant. So what I...
:-pYeah, I suppose it was kind of a silly way for me to phrase my questions. Though I commend you for not only answering the questions I posed but also addressing and answering the questions I meant when I myself didn't fully realize that those alternate questions were far closer to expressing...
First of all, ellipses and hyperbolas both have two foci, not one focus. The two foci are the two points in the definitions I provided, not two other points. So, if the two foci are A and B, and the distances between those foci and any given point P are |AP| and |BP|:
An ellipse (represented by...
Recently, in my calculus two class, we began going over conic sections. After reviewing the definitions of ellipses and hyperbolas - For two given points, the foci, an ellipse is the locus of points such that the sum of/difference between the distance to each focus is constant, respectively - I...
The Michelson-Morley Experiment (as depicted in the scishow YouTube video "The Greatest Failed Experiment Ever") which was used to test for the effects of 'Aether Wind' appears to be almost, if not completely, the same setup as the one used in a gravitational-wave observatory. Why is the success...
Now that we have confirmed the existence of gravitational waves, have the odds of discovering a force carrying particle changed? With my limited knowledge it kind of seems like if gravity is caused by the warping of space-time, which was confirmed by gravitational waves, would mean that there is...
It has been made clear to me that any velocity can be seen as rest mass, meaning that if I observe someone else experiencing time more slowly than me due to general relativity, so long as they do not change velocities, they will see me as experiencing time more slowly than them. I have also...
For example can an object be very conductive to electricity but be a very poor conductor of heat and vise-versa, or is a good conductor of one always a good conductor of the other and a bad conductor of one always a bad conductor of both?
If they are related, then how and why are they connected...