The animated visuals are very cool, but I desperately want to turn them off in order to understand what they depict and reason about it geometrically. A pause button would be greatly appreciated.
The Shape of Inequalities
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Re: The Shape of Inequalities
#12The animated visuals are very cool, but I desperately want to turn them off in order to understand what they depict and reason about it geometrically. A pause button would be greatly appreciated.
That's actually a good advice. Does a separate, "static" screenshot also work?
Re: The Shape of Inequalities
#13The animated visuals are very cool, but I desperately want to turn them off in order to understand what they depict and reason about it geometrically. A pause button would be greatly appreciated.
That's actually a good advice. Does a separate, "static" screenshot also work?
Sure, that would work just as well. Plus, then you get to pick a "good" placement instead of making the user try to find one.
Re: The Shape of Inequalities
#14Earlier quoted context omitted.
That's actually a good advice. Does a separate, "static" screenshot also work?
Sure, that would work just as well. Plus, then you get to pick a "good" placement instead of making the user try to find one.
Ok. I will add them tomorrow. Also I will fix the first animation (b doesn't grow there as it should).
Re: The Shape of Inequalities
#15There’s a whole pile of math like this that kind of lies in this nether land between more advanced than you’ll get in most high school math¹ but less advanced than you’ll get in most college high school math that I was only ever exposed to when I took the classes for my teaching credential. One of my favorite was how cos/sin, tan/cot and sec/csc all can be derived from right triangles on a unit circle with the first…
Weird, in Canada (at least some provinces) I think that's a pretty standard part of both high school and undergraduate maths.
The relationships between the functions are pretty standardly taught, but their derivation from the right triangles on the unit circle less so (other than sin and cos).
Re: The Shape of Inequalities
#16Re: The Shape of Inequalities
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Re: The Shape of Inequalities
#18In case people aren't aware, the inequality of these specific four means is a special case of the more general power mean inequality: https://en.wikipedia.org/wiki/Generalized_mean#Generalized_m...
I think this is not quite right as stated there because the root mean square (quadratic mean) is always positive or 0 while the arithmetic mean can be negative, making it smaller. I guess the inequality only holds for positive numbers.
That's actually one argument for not calling the root mean square a "mean", because a mean should arguably have the property that it is always a number between the largest and smallest value. But the RMS of two negative numbers is positive. (On the other hand, the median would qualify as a mean in this sense, even though it is not a "power mean".)
Re: The Shape of Inequalities
#19There’s a whole pile of math like this that kind of lies in this nether land between more advanced than you’ll get in most high school math¹ but less advanced than you’ll get in most college high school math that I was only ever exposed to when I took the classes for my teaching credential. One of my favorite was how cos/sin, tan/cot and sec/csc all can be derived from right triangles on a unit circle with the first…
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Re: The Shape of Inequalities
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