Hi, I recently heard the two highschoolers came with 9 more proofs (after their first one some years ago) of the Pythagorean Theorem by using trigonometry.

I have seen their first proof and I could follow it just fine, but I cannot grasp how in principle it is possible to prove something by using its own theory (if thats fair to say?).

When I hear someone say that they proved some essential part of trigonometry, by using trigonometry, I just instantly think that is impossible. Clearly its not though so im wondering if someone here can explain to me how how it is possible or what im misunderstanding.

This might be an incredibly weird question but I'd love for anyone to attempt to answer it, however vague it needs to be.

Because of circumstance I have to work in a supermarket with absolutely lovely coworkers. Though thee tasks I have to do are generally mindnumbingly boring: packing, sorting,... Etc.

So to keep my mind busy while packing products in boxes I have been trying to think about the maths related to packing theory on how to fit certain shapes most efficiently into a box.

From there my question: are there any general ideas/rules/tips/whatever that we know from maths (packing theory?) that would be useful to know for someone who has to pack things daily?

Suppose theres just an average supermarket worker packing things and you'd have to give some tips to help him optimize his packing skills, what would you tell him? Which ideas from maths would be useful to know? Suppose he sees some kind of shape that he has to put in a cardboard box, how would you want him to approach the situation? Even besides all this: what, if anything at all, would you give as a tip?

Like I said this might be kind of impossible to answer, but I encourage you to take this as a non-serious question just purely for fun. I will try out anything you can come up with, even things that arent practically useful but just theoretically interesting would be appreciated to keep my mind occupied.

So i am studying some heat diffusion models, i know the terminology is important
but can this coefficient be regarded just as weight, like what is the differences between weight and diffusivity coefficient aside of weight being the general term used in general equations

Or is it just algebra applied "abstractly"? If so is "abstraction" something you can do with any mathematics by definition since all math is abstraction? How abstract does abstract algebra go and what are the prerequisites to understand it?

If I take all the past draws can I find the way how the numbers are drawn ?

I am noobie mathematician, please don't laugh at me. I am trying to learn mathematical analysis on my own. So everyone kept saying that baby Rudin is the way, but his first chapter just throws me off. I understand the material he is showing, and he is trying to sneak in a slick inequality to show that rationals have gaps or incomplete. However, for the love of math I couldn't understand where or how he derived those inequalities at first ‽ I kept going forward and things made sense, like sups and infs, reflexive, transitive properties, etc. But that inequality got stuck on the back of my head like an unfinished business I had, so it kept me turned off from going any further. Primarily the logic I had was that "if I can't figure out that inequality, then I am not worthy of keep on reading this book".

I noticed that when you take a base x and raise it to the power of x however many times, y will be either zero or one when x is zero. What I find interesting is that the y value at x=0 depends on whether the amount of times you raised x to the x is even or odd. I think I’m doing a bad job of explaining the phenomenon, or I’m just over complicating something basic, but I can’t wrap my head around what’s happening. Can someone explain? I’ll put a picture to show what I’m talking about.

Consider the abelian group A(H) of self-adjoint operators over a Hilbert space H. This group can be ordered by setting A\leq B if and only if the operator B-A is either positive or null. This ordering is compatible with addition in the sense that if A\leqB then A+C\leq B+C for all C. Now take the interval [0,I] (this is the subset of positive operators that lie below the identity). Is it true that <[0,I]> (the smallest subgroup containing [0,I]) is all of A(H)? I have a hunch that the answer is 'yes' (at least I'm hoping it is), but I can't quite prove it.

I know that it suffices to show that every positive operator P lies in <[0,I]> because it is known that every self-adjoint operator is a difference of positive operators. The problem I'm having is that while I can show that there's a smallest n such that P-(n+1)I is not positive (which implies that P-nI is positive and as 'close' to 0 as I can get by subtracting I repeatedly) it isn't necessarily true that P-nI is below the identity. I tried some examples and it seems that there are indeed positive P where P-nI remains above I, which isn't very surprising.

Now, regardless of whether my hunch is correct or not, I want to think the original question already has an answer, but evidently I'm not clever or knowledgeable enough to find it myself. I'm not very well-versed in Functional Analysis, to be honest, but my work currently revolves around effect algebras, and the archetype for these structures comes precisely from that area.

Im a grade 12 student who switched from pure math to math literacy due to failing. I would attribute me failing to having a bad teacher and not paying attention in class and failing leading me to have a hatred for math. I honestly think its because i did bad because i actually find math extremely fascinating and would like to improve. And it would also help with my college applications if i take a math course and do well. I was wondering if anyone has any advice or tips to help me become better at math?

Basically, I 'rediscovered' the unit circle for school trig as a useful thing in mathematics and the circle functions. I've been enjoying proving identities and finding interpretations of them geometrically on the unit circle. Is there just a resource of trig identities that you know of that are basically mathematical treats that I obtain enjoyment in proving them and finding interpretations.

I'm looking for the name of a method of using 2D vectors to create 3D illusions (kind of like these football adverts on the field).

I remember learning about it in my high school math class but I can't remember what it's called or how to calculate the correct vectors.

Thanks in advance!

Hello everyone! I got a question during long Time what IS really the poincare conjecture Can you explain it to me plz ? Thanks

I'm referring to the rule that says that, if you double the ones digit of a number and subtract it from the remaining number, the entire number is divisible by 7 if the difference is. So, 833 would be 83-2(3)= 77, for exmaple.

There are explanations elsewhere in this sub, but none layman enough for me. Thanks!

Hi am about to quit my career in maths I think it’s to hard and I think that am not learning enough, because there is other people that it’s brilliant and I compare myself with them. it’s my first semester I want to stay because y love maths but I think it’s to hard, any advice? Please

I've been trying to use Logger Pro for a Maths investigation, where I try to model the flight path of a tennis ball. For some reason when I import the video into logger pro, the quality becomes lower and the frames per second is lower than when I play the video normally in quick time movie. The ball looks incredibly blurry as well in quick time player, does anyone know how to solve this issue? Or is there another resource/ app that is better at analyzing trajectories of projectiles, plotting on a graph and also finding the velocity at each point?

I really want to know because I am trying to be so good at math that I want to do some challenges.

hello guys, I am a first year MSc student in physics and we have this subject called mathematical methods in physics. my undergrad was a dual major degree with physics and chem, I had no math. i am still doing decent, however I need more intuition on laplace transforms. our professor is good but he's kind of rushing through, makes sense because most people must have done it in their undergrad. i feel it's important to visualise things like fourier and laplace transforms in order to understand their applications. i am decent with Fourier, i watched a couple of videos explaining the intuition behind Fourier series, 3b1b was the best. but can anyone recommend some channels or lectures explaining the derivation of the final formula( F(x)= a0/2 + sum an cos(nx) + sum bn sin(nx))? need a bit more intuition on the 1/2 factor with a0. coming to laplace, i don't understand why we're doing it. Google says we're converting a real function to a complex one but why? why do we need to do that? also the whole idea of representing a waveform in terms of sine and cosine, why is it so necessary? i know I am asking dumb questions but please bear with me😭

I am aware that math degrees are better completed in person. However, I do not have the finances or time in order to attend college full time IRL, and math is the only thing I have any intention of getting a degree in. I do have education benefits which will cover my tuition. Should I pursue the online math degree?

Hey guys I’m planning on going back to school soon through an employer so I can finish my math degree. I dropped out about 2 years ago after receiving abysmal grades and now I feel like I’m ready to return. The only problem is that for companies like Papa John’s & Starbucks where 100% of tuition is covered, the partner schools only include online universities with high enrollment (UGMC, ASU online, etc.). How will this look on my application for PHD programs? How can I manage to get research opportunities? I’m positive atp that I want to go to grad school. Thanks for your help!

Hello everyone,

I'm a freshman at college right now (just started a few months ago) and and am planning on double majoring in physics and math. It's my understanding that at least at my college the majors aren't super dissimilar so it wouldn't be many more credits than I would've already had to take to major in one. I really find math interesting, especially the logical deduction, proofs, and esoteric concepts etc. Right now I'm taking an accelerated course that'll give me credit for both calc 1 & 2 (as I already had experience with calc in high school). Was just wondering any advise when it comes to anything relating to this major/career path - I definitely plan on going to grad school as well (although I'm not sure whether for math or physics yet). Anyways, thanks for reading, looking forward to any advise.

Say we are given angle X and length A as our inputs, is there a way to find angle Y?

Given this, if I answer 14 questions right and leave the rest blank, I should be able to qualify for AIME right?

So i’m solving an equation that uses the formula for area of a rhombus. The practice question’s explanation states that the area of a rhombus is A = b x h . When I searched it up on google, it tells me that the formula for area of a rhombus is : 1/2 x d1 x d2. Are these two formulas both the same in terms of getting an answer or is one of them incorrect?

Hi!

i just have a question that's been nagging me for the past hour (for some reason)

I know how to simplify negatives and fractions while distributing, but idk why but my brain is not working right now.

say you have: z -y * ((x-4)/2)
how would you simplify that, or how would your thinking take you through it?

i cant seem to wrap my head around the negatives and such. thanks in advance!

I just took out the following loan:

$13,000 loan, 13.5% APR, 3 year term, no origination fee. Monthly payment = $444.35

My question is this: I may only need to use 7 or 8 thousand. If I immediately pay back $5000 for this loan, but continue paying the same monthly payment, aren't I effectively lowering my interest rate? What does the interest rate become? How do I express this problem mathematically? (P.S. I'm pretty bad at math). Thanks!

I’m doing AMC 12 this year, does AIME floor means the minimum score I need to qualify for AIME?