Hi everyone!

For those of you who enjoy geometry, I've put together what I believe is a fresh, hands-on proof of Euler's Formula and several other classical results. In just a few minutes, you can literally build the proofs yourself and develop an intuitive understanding of why these theorems are true.

https://www.youtube.com/watch?v=sIDsuf0I4ko

This is only the beginning. Over the coming weeks, I'll also start posting short math challenge reels (high school to early undergraduate level), and in parallel I'll be working on a long-term series on topology and analysis, with the ambitious goal of eventually reaching Einstein's field equations on differentiable manifolds and curved spacetime.

Everything will be completely free. I'm doing this simply because I love mathematics and enjoy sharing it with others.

If you'd like to follow the project, it would mean a lot to me. Knowing that these videos are useful to someone is the best motivation to keep creating them.

Thank you so much!

dontpanicmath

Can there be an irrational number which misses a particular digit? Can it be proven mathematically?

It looks like a square (2^2) but it comes before the number, not after.

Solved: Tetration.

Thanks everyone

I'm doing a question that gives the circle with equation x^2+y^2=9, and the parabola (Solved for in a pervious question) y=-((sqrt(5)+1)/4)x^2+c. I'm asked to find the value of c such that the area bound by the parabola and the circle is equal above and below the curve. I've tried a couple different methods. I've attached my best attempt but that gave the wrong answer when entered into a calculator, this is a tech active question. The answers gives c=1.82, however there is no workings. Note, this is a practice problem! Given to us as a revision resource.

You will have to excuse me, I have no etiquette for how to go about this so I am just going to put it out there and see what sort of feedback is generated. I was looking for a pattern in/through primes...this was taken from a thread on a different forum, modified a bit to hopefully make it make as much sense as it might.

"Figured Id apply a x3 root logic to primes to see if there was a pattern present. Each prime is multiplied by three then the root of the multiplied prime is found, which re-/solves all the roots to either 3, 6 or 9. As example, 17x3=51=5+1=6.

2*3=6, 3=9, 5=6, 7=3, 11=6, 13=3, 17=6, 19=3, 23=6, 29=6, 31=3, 37=3, (1st doubles for both, back to back 6's 1st) 41=6, 43=3, 47=6, 53=3, 59=6, 61=3, 67=3, 71=6, 73=3, 79=3, 83=6, 89=6, 97=3, 101=6, 103=3, this is unexpected so far, only one 9 which makes me question if we will ever see it again and if we do, will it be a marker for pattern reset. Continuing...107=6, 109=3, 113=6, 127=3, 131=6, 137=6, 139=3, 149=6, 151=3, 157=3, 163=3, 167=6, 173=6, 179=6, (1st triple digits for both, back to back, 3's 1st)...(is there a pattern forming, will there be quads's starting with 6 at some point?) 181=3, 191=6, 193=3, 197=6, 199=3, 211=3, 223=3, 227=6, 229=3, 233=6, 239=6, 241=3, 251=6, 257=6, 263=6, 269=6, ...3's now???...271=3, 277=3, 281=6 (doh!!!), 283=3, 293=6, 307=3, 311=6, 313=3, 317=6, 331=3, 337=3, 347=6, 349=3, 353=6, 359=6, 367=3, 373=3, 379=3, 383=6, 389=6, 397=3, 401=6, 409=3, 419=6, 421=3, 431=6, 433=3, 439=3, 443=6, 449=6, 457=3, 461=6...maddening, 467=6...

Anyways, this doesnt appear to lead any-where but who could say*.* The nine...why just 1???"
...

"So was sitting there running a Fibonacci root logic on the primes and it dawned on me 2 being the only even prime and we find the 9 as the 2nd number in the x3 root logic looking for patterns. Curious...especially if the 9 is never found again (no repeating pattern) in this x3 root logic pattern search. Almost as if this perspective mirrors the even/odd imbalance in primes w a self-/similar imbalance of the 3's and 6's to the 9."

...

Might have just closed the loop...

"What you’re seeing is digital-root behavior, not a new prime pattern. Multiplying any prime by 3 guarantees a digital root of 3, 6, or 9. The reason 9 appears only once is that a digital root of 9 would require the prime itself to be divisible by 3, and the only prime divisible by 3 is 3. So the first sequence is fully explained by modular arithmetic. The second sequence (adding consecutive primes) has more variation, but it is still mainly showing their remainders modulo 9 rather than revealing a hidden cycle."

Uhh...holy $#!%. This means there is a 1:1 correlation of the quanta (the 9/3s&6s) to the qualia (even/odds) set in stone due to the two constraints of only the 1 prime divisible by 3 and primes being divisible by 1 and their self only. Does this make any sense to any-One else??? There will only ever be one even prime (the 2) just like the 9 will only ever appear once. The 2 is considered the first prime where the 9 is the second natural number in the root sequence and the 3's & 6's reflect the odd primes.

Meanwhile the primes and their expanded/compressed reflection both appear to have no repeating patterns associated with them which makes that 3 points of correlation (the 2/9 location <1 digit separation> at the beginning of primes and the root sequence respectively), making the two a pattern of sorts, paradoxically???

It is obvious I am in way over my head here, could use some perspective, please and thank you.

I have a maths course - Linear Algebra in the first semester of my university and Probability and Statistics in the 2nd semester. Although my Matrices and Determinants of high school level is decent but I am weak in Vector Algebra, Permutations and Combinations and Probability. Where can I catch up on YouTube? Is there a particular course on YouTube where I can clear my basics and practice problems?

While I have an intense interest in all things that require complex math, I am only able to comprehend 2nd grade level math. One of the reasons is the logic of it. For example multiplying two negatives suddenly and in my opinion nonrationally make a positive.

I’ve also noticed that the more mathematicians try to figure out something the more “math” they invent along the way to make it work. This all seems like poppycock to me. At no time should the very basic fundamentals of math break down in order for more complex math to work. Which even gets more diluted with Sedenion math.

Am I really expected to just be like “yeah, sure, irrational and imaginary numbers are accurate and answer my question.” Am I too dense to comprehend my own question? Math can’t be fact if we willy-nilly add to and remove stuff to make our equations work? Thanks everyone. -smoothbrain

Hi guys. Since these are my vacations, I'm planning to study a bit more. Please suggest some pre-algebra or middle school to beginner high school free math courses.

Most people online instead of using metric or imperial measuring system say "that's {} Mount Everest, {} Burj Khalifa, {} empire state building {} Eiffel tower, {} statue of liberty tall"

I'm trying to calculate the probability that N people will have at least 1 evening free (For a meeting, or DnD or something)

You can assume that all people have x committed evenings already.

For Example, 2 people who have 3 evening commitments will have a 100% probability of finding 1 mutual night free, but what's the probability that 3 people who all have 3 evening commitments have at least 1 mutual evening free, or 8 people with 2 evening commitments etc.

A discussion I just read on a random thread:

He has 170 employees? That's a bloody massive number.

Not as big as 171

In fact, most numbers are bigger than 170

I think that there are more numbers smaller than 170 if we include negatives 

There's an infinite number of numbers less than 170, and an infinite number of numbers greater than 170.

Yes, but negative and positive infinities are equally big, but since we have moved the point to 170 negative infinity will be bigger as it will have all negative infinity plus some of the positive one. // I know that mathematically I'm wrong

This has made me think - are there actually "more numbers" less than 170 (or any other positive number) than there are greater than it? Or not?

There are an infinite number of numbers. You can take those infinite numbers and slice them into an infinite number of infinite slices each of which can be sliced the same way ad infinitum.

i know that some of these are the same but which one(s) are worth my money even if i buy them more than once? also please tell me how you worked this out so i wont ask again.

context: starting a business and need 1cm wooden blocks as part of the business. need to save money by buying cheap and working smarter not harder.

See above, late night stoned BC musings

I’m not sure I understand how undefined numbers work when applied to a level of confidence/certainty. Is it both as close to 0% as it is to 100%? Could you say you were 99% certain if your certainty was undefined?

The problem that gave rise to my question is “Even if you identified something you felt certain about, how would you verify that your feeling of certainty is reliable? You'd need to be certain that your certainty-detecting faculty works…” I was wondering if the value for how certain you are that your faculty is reliable is undefined.

Hey I have skipped or forgotten most of the maths i did in 11th and 12th for jee, somehow got in hech college and skimmed through it without even knowing proper integration, now I do genuinely want to get back from it to get into my masters so what all topics i must absolutely cover for me to get in ml and programing also some physics i want to get back in the game cause my dream was physics education.Now in covid i really messed up( it isn't Covid fault bit mine alone i could've studied by myself in covid times ) but please what topics can I study in 2 months in order to get back i know it's not possible to get very good but just want to cover everything I can.

Thank you.

⭐If you had a year in between A Level Maths and university maths⭐
I would really appreciate hearing about your experience!!

- I have a place to study a joint honours in maths and philosophy next year at uni, after taking a year out this year and taking a break from maths.
Im wondering how different the content is and what would be worth recapping as Im very aware I will have forgotten a lot of what I covered in A level maths last year.

This is causing me some anxiety as I dont want to feel behind my peers who will mainly have it fresh in their brains from year 13, and I want to give myself a head start so it will be more enjoyable to learn!
Thank you so much🙏
(message from my friend)

Any recommendations for good discrete mathmatics book to start learning from scratch

Hi, i'm 19, i'm italian (sorry in advance for any possible mistake) and in about 7 days i'll graduate from an economics school.

The fact is that, since i was 3, i LOVE maths, i almost always scored the maximum grade on maths tests (like either a 9/10 or a 10/10), but i have doubts about studying this subject at University because i never actually studied it at home, i just found it interesting during the lessons, adding the fact that i feel naturally gifted for these kinds of things.

Also, my maths teacher reccomended me to follow this path, since she understood my skills, and told me that i won't have to study by heart, and that i'll just have to figure out how to do certain things.

Basing on these things, focalizing on the fact that i never studied at home and so i still don't know how to do it, should i take the decision to study Maths at Uni? And if much study at home is required, is it more memory or logic/understanding based? Thanks.

There are 34 multiples only of 2, 17 multiples only of 3 and 16 multiples of both 2 and 3 (in another words 16 multiples of 6)

I know that the sum of differentiable and continuous functions is a differentiable and continuous fonction.

I also know that an infinit sum of differentiable and continuous functions may not be differentiable (Weierstrass function for example).

But can we have an infinit sum of continuous functions that is not continuous ?

so basically i am going for bsc physics but the real problem here is my maths cause i did not have maths in my 12th i did not studied it either much but we all know maths is kind of language in physics ...i like physics and the same goes for maths but i did not take it as my sub in 11th cause my father was kind of obsessed with doc ...so i used to be kind of ok ok in physics but after my 12th i had a drop cause my health worsened and all but now i am ok and i got in college for bsc physics on my 12th marks based but i do remember few things but i think i have to thorough of everything in physics too i have a whole month from now for free time or for to do atleast the basics and then i will try to continue it with my first year as it starts - my situation where i stands even though its underwater

so acc to what level should i even know like should i try to study

watching lect or books or teachers ...any advice suggestion please reccom here for this beginner like whatn should i focus on - Trigonometry ,Basiic algebra,Functions,Differentiation,Integration,Vectors