41–50 of 179 posts
`Θ^i = 1` does make this really slick, imho. I often wonder if someday when we meet alien intelligences, they'll have a completely different set of constants, derivable from our own but different. Θ=535.491... may be such an example.
`Θ^i = 1` does make this really slick, imho. I often wonder if someday when we meet alien intelligences, they'll have a completely different set of constants, derivable from our own but different. Θ=535.491... may be such an example.
1^{x/λ – νt}
with no particular ambiguity or even parentheses. The choice of constants should give you some pause though—we don't have a great way to talk about "true wavenumber" k so we have to talk about wavelength, and we use "f" for a lot of other things while Greek nu looks like an English V so that can sometimes be confusing... it's not _bad_ but it's weird enough that it's not obviously better.
Earlier quoted context omitted.
Fundamental sounds like a value judgment. Pi is transcendental. 2 isn't. That's really the distinction. Unless there were other finite factors in pi, that is the number that's always going to have to be approximated in computation.
"Tau is transcendental. 0.5 isn't." It's definitely a value judgment. But the value judgment is: Is the radius or the diameter more fundamental to a circle?
Why not use Darians? http://proper-pi-manifesto.com
You should call it d/dx bar. Anyway, I love the choice of theta because a while ago I came up with a nice notation for sin and cos and this fits it really well. When I first learned trig, it was by way of skipping into physics early. I only understood cos as the magic button for getting x components from angles, and y as the button for y components. So my notation is based on this very literal brute understanding. Al…
Or put the modifier on the denominator so that the product and chain rules are obvious (the modifier only persists on the dx, not on the dy)
You can also eliminate the constant in some of the integral formulas by using đx instead of dx. I'm surprised the author does not propose this. However, some constants will still remain. Most conspicuously, the 2π constant in the very definiton of the Fourier transform. I once took a personal crusade to eliminate all such constants in the elementary Fourier formulas (plancherel-parseval, convolution theorems, commuta…
Let é = e^sqrt(2pi), déx = dx/sqrt(2pi), and we have
int_{R}(é^(int_0^x(t dét)) déx)
= int_{R}(e^(sqrt(2pi) x^2/(2 sqrt(2pi))) dx/sqrt(2pi))
= 1/sqrt(2pi) int_{R}(e^(x^2/2) dx)
= sqrt(2pi) / sqrt(2pi)
= 1
Earlier quoted context omitted.
Thing is, angles don't really have units (the technical term is they are dimensionless). They are a length (the subtended arc of a circle) divided by a length (the radius of the circle). When you want to do something like get a sine wave of period T, you inevitably have to include a 2π somewhere. Speaking as someone who had to write down many 2π's in university (especially as I find angular quantities like angular fr…
Angles aren't dimensionless any more than lengths are dimensionless (feet per second makes just as much sense as rpm). It's just that angles have symmetries that lengths don't, which is where 2 pi comes in. Do you want units where your symmetries are expressed in multiples of 1, 2, or 2 pi (for turns, half-turns, and radians, respectively)?
Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my screen reader sees for this page: Recently, I came up with a trick that can get rid of in many cases. It’s pretty simple, but it has some interesting implications. This is the trick: I just define a new derivative operator, like so: That’s all. You just take the…
But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)
Earlier quoted context omitted.
Angles aren't dimensionless any more than lengths are dimensionless (feet per second makes just as much sense as rpm). It's just that angles have symmetries that lengths don't, which is where 2 pi comes in. Do you want units where your symmetries are expressed in multiples of 1, 2, or 2 pi (for turns, half-turns, and radians, respectively)?
Angles are absolutely more dimensionless than lengths are. For an easy check you can't add quantities where the dimension differs, which means it doesn't make sense to add a length to its cube. On the other hand it does make sense to add an angle to its cube - this is a necessary component of computing sin(angle) by the power series sin(angle) = angle - (angle^3)/6 + ...
360 - (360^3)/6 = -7M degrees
2*pi - (2 * pi)^3 / 6 = -35 radians = -2k degrees
1 - (1^3)/6 = 0.8 turns = 300 degrees
Unrelated to the content but complaining about the website is a popular thing to do here so I'd like to share my experience, as a blind user. Here is what my screen reader sees for this page: Recently, I came up with a trick that can get rid of in many cases. It’s pretty simple, but it has some interesting implications. This is the trick: I just define a new derivative operator, like so: That’s all. You just take the…
But what is the answer? What should I do differently? I get don't use images, but then what? I can't imagine all screen readers have the same capabilities, or that there is a base common ability, so what should we do? Googling says MathML is the answer (e.g. https://www.washington.edu/doit/how-do-i-create-online-math-... this site uses MathML and your reader isn't handling it. So now what? (alt-tags? something else?)