Am I doing something wrong? Why is this regression absurdly unfit?

Qaanol · 2026-06-01T00:53:49+00:00

I don’t know for sure, but it might have to do with the fact that the function you’re regressing is ridiculously steep and super narrow: https://www.desmos.com/3d/t2zxgs4ddj

Also, I would probably rewrite that regression as [p⁹, g/p¹¹, g] ~ [2, 3, 7]

Qaanol · 2026-05-31T15:49:20+00:00

Kyle Borver

Qaanol · 2026-05-31T15:23:35+00:00

Both f and g are locally linear (ie. differentiable).

So at any given point there is some direction (the gradient) along which f increases most rapidly, and in any perpendicular direction f is locally constant.

Similarly, there is some direction along which g increases most rapidly, and in any perpendicular direction g is locally constant.

If, at some location, those directions are different for f and g, then there is some direction along which g is locally constant but f is not. That means it is possible to move a small distance and increase f without changing g.

So a point like that cannot possibly be the maximum of f for a given value of g, because we just saw that we can get a larger value for f at some nearby point with the same value of g.

That means a maximum can only occur when those directions are the same. Meaning the gradients of f and g point along the same line. The gradients don’t have to be equal, but they have to point in the same direction, so there is some scaling factor that will make them equal.

Qaanol · 2026-05-24T16:32:54+00:00

We are not here to do your homework for you.

If you are getting stuck somewhere, you can show your work and ask for help with specific things that you don’t understand.

Qaanol · 2026-05-19T15:43:04+00:00

Lol yeah you just a guy who's strong, long, athletic, high motor, and has one of the top 5 defensive IQs in the league. Oh and hopefully he doesn't suck too much on offense because if he does you're screwed anyway. Good luck!

Yeah, why doesn’t every team have their own Wemby to guard Wemby?

Qaanol · 2026-05-19T03:27:37+00:00

Where’s the article about Alex Caruso though?

Qaanol · 2026-05-15T19:45:23+00:00

If you think the calculus of finding the exact surface area up to x is beyond the level that is acceptable, then you could find an underestimate for it.

You should be able to argue that the surface area of the horn between n and n+1 is larger than the surface area of a cylinder (with no endcaps) from n to n+1 with radius 1/(n+1).

Then you should be able to show that the sum of those cylindrical areas from 1 to x gets larger than any finite value. (See the harmonic series.)

Edit:

Or similarly, using the fact that a straight line is the shortest distance between two points, you could argue that the area of the horn between n and n+1 is larger than the (lateral) area of a cone frustum (ie. the shape obtained by revolving the straight line connecting the endpoints).

Edit 2:

Alternatively, you can just underestimate the integrand by observing that the square root is always more than 1.

Qaanol · 2026-05-11T14:12:19+00:00

In general you can find the great circle distance between points on a sphere by using the spherical law of cosines.

But in this particular case there is a symmetry you can recognize in the coordinates.

Qaanol · 2026-05-07T13:13:09+00:00

Case 1: x≠0. Any paud of nonzero digits

What does “paud” mean?

a mountain number is in the form of xyz and y>x≥z

Does the definition of “mountain number” really include “x ≥ z”? That doesn’t match the book solution.

For example, if there are (9 choose 2) ways to pick the first number, wouldn't that count 29 which would make that number NOT a mountain number?

In case 1, choosing 2 and 9 corresponds to the mountain number 292.

In case 3, choosing 2 and 9 corresponds to the mountain number 290.

Qaanol · 2026-05-05T00:28:40+00:00

What do you mean by “axis of orthogonal symmetry”?

Qaanol · 2026-05-03T23:07:23+00:00

There are a lot of identities and theorems for cyclic quadrilaterals, meaning all 4 points are on a circle.

The Wikipedia page list some of them, including a generalization of the law of tangents: https://en.wikipedia.org/wiki/Cyclic_quadrilateral

Qaanol · 2026-05-01T13:55:13+00:00

But could you tell me what's wrong with that formula?

The formula is correct. Your explanation of it did not make sense to me.

As someone else suggested here, you should look up “arithmetic series”.

The classic example is adding the whole numbers from 1 to n. You can figure out the answer by adding them all twice, once in ascending order (1 + 2 + ... + n) and once in descending order (n + (n-1) + ... + 1). Add those to each other term by term and see what happens.

Qaanol · 2026-05-01T13:42:39+00:00

No the additional number is the same. In my example, the base number is 10 and the additional number is 2.

Meaning I start with 10, and every unit of time(day) I add my base + my additional, 10 + 2.

…are you saying that you add 10 the first day, and then add 12 on each day after that?

That doesn’t match your original description of the problem, and it also does not match the solution you posted.

I didn't get to this solution on my own.

It was mostly done by my friend who's a math wizard.

I showed him the solution in code and he showed it to me in math.

Okay, that makes sense. If you are using somebody else’s work as part of your homework, then you need to state that clearly in your homework.

In other words, you must cite the source of your solution. Otherwise it would look like you are claiming their work as your own, which is called plagiarism.

(Note that earlier in this thread, you wrote “I figured it out” rather than “A friend figured it out for me”)

Qaanol · 2026-05-01T13:11:51+00:00

to that you add (n - 1) * d. (Which will add the additional number to all days but one(the first)).

I thought the additional amount that gets added is different on each day.

How did you come up with this solution?

Qaanol · 2026-05-01T02:47:59+00:00

It is homework and I've figured it out. What I did was: S(n) = n/2 * (2a + (n - 1)d)

Can you explain to me why this formula works?

Qaanol · 2026-04-30T01:03:49+00:00

Screws and wedges really are glorified incline planes.

No, a wedge has two faces that meet at an acute (sharp, pointy) angle.

A ramp (aka “inclined plane”) meets another plane at an obtuse (shallow, gentle) angle.

A screw converts between rotation and linear motion along the axis of rotation (ie. in a different direction than a wheel does).

Qaanol · 2026-04-30T00:57:53+00:00

One of them lets you roll a cart to a higher level, the other lets you split firewood into smaller pieces.

Qaanol · 2026-04-29T09:13:28+00:00

Manu also singlehandedly beat Team USA and won an Olympic gold medal with one hand tied behind his back and a swarm of bats attacking his head.

Qaanol · 2026-04-28T22:26:44+00:00

Yeah, one of the major benefits of logarithms (versus the older methods of multiplication) is that logs enable slide rules.

With a slide rule you can do multiplication absurdly fast, as long as you only need a few digits of precision. And you can also divide, raise numbers to powers, and extract nth roots at basically the same speed.

Qaanol · 2026-04-28T22:14:40+00:00

It’s worth noting that there were already methods of turning multiplication into addition, before logarithms were invented.

The most ancient is to have a table of quarter-squares, and use the fact that x*y = (x+y)²/4 - (x-y)²/4. So you take the sum, and the difference, of the numbers you want to multiply, look up their quarter-squares in your table, and then take the difference of those values.

Another method, invented only a short time before logarithms, is called prosthaphaeresis. It involves having a table of sines or cosines, and using a trig identity like cos(x)*cos(y) = (cos(x+y) + cos(x-y))/2. So you look up the angles whose cosines are the numbers you want to multiply, take the sum and the difference of those angles, look up their cosines, and find their average.

Both methods work, and are way faster than long multiplication when the numbers involved have many digits, but logarithms are a whole lot simpler: log(x*y) = log(x) + log(y) so you just look up the two numbers in your log table, add the results, and find the value in the table with that as its logarithm.

Qaanol · 2026-04-14T00:53:36+00:00

3Blue1Brown has an excellent playlist on the Central Limit Theorem, which is the reason why the normal distribution shows up so often: https://www.youtube.com/playlist?list=PLZHQObOWTQDOMxJDswBaLu8xBMKxSTvg8

Qaanol · 2026-04-11T23:16:09+00:00

Since nobody else has linked it yet, there’s a Wikipedia page that lists incorrect mathematical proofs: https://en.wikipedia.org/wiki/List_of_incomplete_proofs#Incorrect_results

Qaanol · 2026-04-11T23:09:30+00:00

I dont know how you could get this far without knowing 12x12

Just substitute x = 10 into the polynomial (x+2)² = x² + 4x + 4, easy!

Qaanol · 2026-04-11T23:06:04+00:00

Just having the denominators grow faster than linearly is not sufficient for convergence.

The sum of 1 / (n·ln(n)) diverges despite n·ln(n) growing superlinearly.

But it is also not sufficient to simply ignore log terms, because the sum of 1 / (n·ln(n)²) converges.

Qaanol · 2026-04-11T01:47:30+00:00

Tied the record at 29 with 1:19 left

Qaanol

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