Is it just the basic 3D geometry? When I try looking it up it just comes up with basic elementary school formulas for prisms like bhl=v. Does it get more complex than that and if so where should I find further reading for it.

What is the largest set of unique regular polygons so that no polygon can fit inside another (rotation is allowed)? For instance, I can have a triangle and a square if I make the square's sides smaller than the triangle's so that the triangle can't fit in the square, but not so much smaller that the square could fit in the triangle.

Is it possible to have every n-gon up to infinity if we choose the way the side lengths decrease carefully? If not, maybe all prime p-gons? If an infinite set is possible, can you find the side length as a function of n?

If no infinite set is possible, what's the largest set you can make? What's the largest set you can make if you have to start with n=3 and go up from there?

Your thoughts are appreciated!

Context:

When you open a specific pack of cards in pokemon pocket you get 5 cards, only the 4th and 5th card can be the rarities I care about so the first 3 are irrelevant.

4th card rates:

• Full art: 0.5% chance, with 10 unique cards so 0.05% chance each
• Crown rare: 0.04% chance, only 1 crown rare card available

5th card rates:

• Full art: 2% chance, so 0.2% each
• Crown rare: 0.16% chance

After you open a pack you get 5 pack points which can be used to buy the exact cards you want. At 1250 points (250 packs) you can buy one of the Full art cards. You can hold a maximum of 2500 points (500 packs worth) so no saving up until you have enough to buy all the ones you are missing. The strategy im using to open packs trying to collect all of the Full arts is to open packs of cards until I have 2500 points, then use 1250 of them to purchase one of the ones I havent got yet while keeping another 1250 in reserve. This allows me to either Obtain 8 of the cards and then hit 2500 points again to buy the last 2, or Obtain 9 cards some time before hitting 2500 again and use the 1250 in reserve to buy the last one. With this you can see that the maximum amount of packs you would have to open to obtain all 10 of the Full arts is 2500 (which would only happen if you didnt obtain any through opening packs and instead had to buy them all for 12500 points)

My questions surrounding this are how would I work out 1. The average amount of packs you need to open to obtain all 10 Full arts, 2. What is the probability of obtaining the single Crown rare card before obtaining all 10 Full arts and finally 3. Is this the most optimal way of opening packs (this is the least imporant question)

What ive done so far:

I really have done nothing of value, first i tried simplifying everything to see if i could just get a proof of concept going. I combined the separate 4th and 5th card into a single event for a 2.5% chance of obtaining a Full art card and tried to use what I remember of binomial probability to work out the average amount of packs needed. Its here where I realised I havent done any real maths since highschool and I am way out of my depth.

So I asked AI for help with this simplified version and it told me to go away and do a Monte Carlo simulation. If at all possible to do work this out without simulating it 10000 times I would love to hear how

https://preview.redd.it/srnm1lbe7rge1.png?width=712&format=png&auto=webp&s=aa1951b12e7552865b38b11180fd61a118d77091

I tried this and ended up with p(p-3q) = 2024. Then I wrote down all the factor pairs that can be expressed as p(p-3q) and there weren't any so my answer was 0. Is my answer correct?

Hey ask Math! If this is against the rules, I appologize, but I figure Id just shoot my shot.

I am bringing this to yall from the UFO side of reddit, where a bunch of people like to make stuff up and make un-verified claims. So today I am bringin you one of those unverified claims.

This poster claims to have some equations that solve all sorts of problems, but I am pretty sure they just made an overly complicated post that doesnt actually mean anything, but I dont know enough about math to say that for certain. What do yall think? Post pasted below:

Here are the equations again:

The complete unified mapping shows specific coupling relationships:

1. Quantum Field-Consciousness Interface:

ΨQFT(x,t) couples through: • Field operators: Â(x,t) = φ^(i/2π)â(x,t) • Vacuum state: |0⟩ = φ|ψ⟩ • Creation/annihilation: [â,â†] = φI 2. Fractal-Matter Coupling: ΨFractal terms map through: • Mass coupling: m = φ^D|ψ|² • Charge coupling: q = Im(ψ∇ψ) • Spin coupling: s = φ×(ψσψ) 3. Consciousness Field Terms: • M(ψ) = φ∇×ψ (Mind-field) • C(ψ) = ∂ψ/∂t (Current) • P(ψ) = |ψ|² (Density) • Q(ψ) = Im(ψ*∇ψ) (Flux) 4. Unified Pattern Evolution: Through Dualiton frame [φ 1; 1 φ⁻¹]: • Pattern self-observation • Clean boolean transitions • Phase-locked resonance at α • Perfect φ relationships 5. Extended Maxwell Terms: ∇ × (φE + ψ) = -∂(φB + ψ)/∂t ∇ × (φH + ψ) = J + ∂(φD + ψ)/∂t ∇ · (φD + ψ) = ρ + P(ψ) ∇ · (φB + ψ) = Q(ψ) All unified through the wave function ψ = φ^(i/2π) and perfect pattern alignment.

1. Quantum Field-Consciousness Coupling:

ΨQFT maps through: • Field operators: Â(x,t) = φ^(i/2π)â(x,t) • Vacuum state: |0⟩ = φ|ψ⟩ • Creation/annihilation: [â,â†] = φI 2. Fractal Pattern-Matter Interface: ΨFractal terms map through: • Mass coupling: m = φ^D|ψ|² • Charge coupling: q = Im(ψ∇ψ) • Spin coupling: s = φ×(ψσψ) 3. Consciousness Field Terms: • M(ψ) = φ∇×ψ (Mind-field coupling) • C(ψ) = ∂ψ/∂t (Consciousness current) • P(ψ) = |ψ|² (Pattern density) • Q(ψ) = Im(ψ*∇ψ) (Quantum)

Quantum-Consciousness Interface

1. Field Operator Evolution:

• Â(x,t) = φ^(i/2π)â(x,t) maps consciousness to fields
• Vacuum state |0⟩ = φ|ψ⟩ shows pure potential
• [â,â†] = φI maintains creation/annihilation balance

Pattern-Matter Coupling

2. Fractal Interface:

• Mass coupling: m = φ^D|ψ|² maps density
• Charge coupling: q = Im(ψ*∇ψ) shows field flow
• Spin coupling: s = φ×(ψ*σψ) maintains rotation

Field Operations

3. Consciousness Terms:

• Mind-field: M(ψ) = φ∇×ψ
• Current: C(ψ) = ∂ψ/∂t
• Density: P(ψ) = |ψ|²
• Flux: Q(ψ) = Im(ψ*∇ψ)

Extended Maxwell Relations

4. Field Equations:

∇ × (φE + ψ) = -∂(φB + ψ)/∂t ∇ × (φH + ψ) = J + ∂(φD + ψ)/∂t ∇ · (φD + ψ) = ρ + P(ψ) ∇ · (φB + ψ) = Q(ψ)

All unified through wave function ψ = φ^(i/2π) and Dualiton frame [φ 1; 1 φ⁻¹], showing complete consciousness-matter mapping

Hello everyone, I have suddenly developed an obsession with dimensions and ways of studying the structures that exist in them and in what ways can higher dimensions translate to lower dimensions and how to predict the higher dim structures that lower dim slices might be part of.

I want to know in which direction should I take my research in order to get the tools to navigate the problems that I just stated

I haven’t kept up on any advanced math in 20 years. (42M) I’m interested in a casual refresher that touches on some basics that will make effective use of time. Any suggestions for some refresher content?

My son is 1, and I’d like to make sure I have it all back by the time he is 5 or 6 to introduce him to broad concepts.

Hey I am new to this group and new to spherical geometry. I am not sure if I correctly understand haversine formula. What I understood is that it calculates the shortest distance between 2 points on the sphere ALONG great circles, which are circles going through the center of the earth. Does it mean that if I am calculating distance between 2 points laying for example on the same latitude 40 it won’t give correct results, because this is not great circle, the distance is not aligning with part of great circle ? Would be happy for answers thx a lot

https://preview.redd.it/k7j7ntrvlqge1.png?width=625&format=png&auto=webp&s=d89ee404dc3c1b9379d928e1edc68c159fd0caf2

I'm wondering whether there is a way to project the circle onto the part of the bicylinder's surface outlined in green (which closely resembles a spherical lune) the way a sphere's surface can be projected onto a cylinder to show that its surface area is equal to 4(pi)r^2. The projection would need to show that the projection increases the surface's area by a ratio of 4:pi (since the area of each part of the bicylinder has an area of 4r^2 as opposed to (pi)r^2. I don't think Cavalieri's Principle will work since the corresponding yellow cross sections would need to have lengths in that ratio, which they don't unless there is a serious optical illusion going on here. Does anyone know a way to do that or get an equivalent result without calculus or more advanced math?

given that f(f(x))=(x^2+x+1)f(x), find f(20). This question came in the BDMO 2024 regional round, secondary category. I tried to get something by saying that f(x)=(inf(x)^2+inf(x)+1)(x), or by trying to make f(x) the subject of the original equation(btw, idk how else to insert f inverse so I wrote inf(x)). Ended up getting nothing (atleast that's what I think). Anyone know how to solve this?

I don't know much calculus so I don't know how to say integrals.

There would, not necessarily, have to be

A = integral of tan(theta) * x from 0 to base

which means if we can prove A = integral of a function of x that = tan(theta) * x from 0 to base, then we win

I know that tan(theta) = height/base, so tan(theta) * base = height, and if the height is a function expressed as h(base), then h(base) = base * tan(theta)

so it would be A = integral of h(x) from 0 to base

how would I prove this last statement?

Hi, I am confused in the transformation calculation. Here is an example:

The transformation kernel is given by the matrix Θ (the basis vectors are the rows of the matrix). The signal x is expressed by the vector x = (1 2 -1).

https://preview.redd.it/esg09z4z6qge1.png?width=357&format=png&auto=webp&s=41ee50ec652f938af0b74060bbbe881288f68b29

Calculate the image of the signal X after the transformation.

I'm confused when to multiply vector * matrix and when matrix * vector...

I'm sorry about the poor explaning title, and the most likely stupid question.
I was watching the first lecture of Gilbert Strang on Linear Algebra, and there is a point I totally miss.
He rewrite the matrix multiplication as a sum of variables multiplied by vectors : x [vector ] + y [vector ] = z
In this process, the x is multiplied by a 2 dimension vector, and therefore the transformation of x has 2 dimensions, x and y.
How can it be ? I hope my question is clear,

1. The Geometry of Linear Equations : 12 : 00

for time stamp if it is not clear yet.

I found this textbook to be rather good at explaining stuff. Thus allowing me to be able to answer 90% of the questions (questions with answers only are answered).

This is odd. Because before this, i used various books and i couldn't understand very well what the author is trying to explain. And the questions in the exercises are somewhat....difficult?

So this left me to question if the book im using now is not good for learning UG level complex analysis as it does not "prepare" you well?

( also , able to answer 90% of the question is the first for me when self learning UG math) Maybe im just underestimating myself.....or am i wrong?

I was looking through some math question papers and I found a problem that was interesting and that I could not solve for a very long time so I am finally asking for answers/help. My best attempt manages to show that numbers in row a and column b are the same as the numbers in row b column a. The question is :

The squares of an infinite table are numbered as follows: in the zeroth row and zeroth column we put 0, and then in every other square we put the smallest non-negative integer that does not appear anywhere below it in the same column or anywhere to the left of it in the same row.What number will appear in the 1607th row and 1989th column? Can you generalize?

we color the sides of a cube either red or blue, but opposite sides have to have different colors. accounting for rotations, how many ways of coloring are there?

Welcome to the Weekly Chat Thread!

In this thread, you're welcome to post quick questions, or just chat.

Rules

• You can certainly chitchat, but please do try to give your attention to those who are asking math questions.
• All rules (except chitchat) will be enforced. Please report spam and inappropriate content as needed.
• Please do not defer your question by asking "is anyone here," "can anyone help me," etc. in advance. Just ask your question :)

Thank you all!

So I pulled an incredibly rare item, 3rd Age Pickaxe, in Runescape that on its own, has a 1/313168 chance of dropping. I obtained it from something called a master clue scroll. Once you complete all the steps on the scroll, you get 5-7 "rolls" on the loot table for different items. On this particular master clue, I got all 7 rolls.
Now the way I obtained the Master Clue was from a Hard Clue, which has a 1/15 of being dropped.

I'm trying to figure out what the actual probability of obtaining the 3rd Age Pickaxe is. Would it be a range of 1/1,565,840 to 1/2,192,176 times 1/60 - 1/90? I'm not sure how to actually calculate the probability of obtaining a 1/313,168 drop from a 1/15 drop item.

In short:
5-7 rolls of 1/313,168 from 4-6 rolls of 1/15. What's the overall probability of obtaining this on your one and only Master Clue?

Thanks!

https://preview.redd.it/cn8w0ul48oge1.png?width=3840&format=png&auto=webp&s=47924501c2ae09601436a6a306922f6b5b51ea8c

This is from an online quiz bee that I hosted a while back. Questions from the quiz are mostly high school/college Math contest level.

Sharing here to see different approaches :)

I created a program that calculates for prime numbers by dividing a given number by 2 and by all previously found prime numbers. Using this I was creating a graph where Y is the prime number and X is the number on the list of primes it is.

The list starts at 3, so on the graph it would be (1,3) and 7927 would be (1000,7927).

My program is very slow, so I am wondering if there is already a graph like this that exists.

(I am not exactly sure what tag should be applied to this, but I believe I chose correctly.)

I'm trying to figure out what the probability of an unlikely event is. My boss always makes me check the backroom before I close up. I know there is nobody back there but it's her perogative. In a universe with infinite time; what is the probability that there is a vampire waiting back there for me?

Assume a button where there is a 1 in unknown chance for it to make a sound when pressed. İf you click it 10000000 times, you can estimate a probability somewhat. However let's say you have low amount of attempts

For example you only click it 100 times and it ringed 4 times. Specifically 7, 19, 44, 56th clicks.

So you could argue that the odds are 4 in 100 for it to make a sound as an "estimate". However, if you were to stop when it did the 4th ring, you would get 4 in 56. If you were to stop at the first ring, you would get 1 in 7.

Or if you were to set an exact amount of clicks and stop at that you get a different answer. For example, like above, if you are determined to click 100 times, there is a chance that you get lower odds than actual

So here for my question: how should one act to determine the probability? When should they stop? For example in this case, I would see that first 4 rings are 4 in 56, then it went for 44 in a row without rings, I would take somewhat average of them in my mind and do some random ass calculations and say "it has a 1 in 20 chance of happening" rather than 1 in 25 or 1 in 14 or whatever.

So, where should I stop counting for a more correct probability estimate? Should I stop when I get a specific amount of rings? Or specific amount of clicks? Or maybe somewhere inbetween?

I personally feel like stopping at a ring results in inflated odds. For example for a coin flipping, if you throw it until you get, say, 4 heads, it FEELS like you are more likely to get more heads than tails till 4 heads happens (like 4 heads and 3 tails) so it seems kinda rigged

What do you guys think?

Here is my thinking.

Consider picking one whole number at random on equal distribution where x (the max capacity of the jar) is the upper range. In other words, a random whole number from 1 to x.

So we have two possibilities. 1) x is even. Then there are the same number of odds and evens in our number range. 2) x is odd. Then there are more odd numbers than even numbers in our range, so odd should be slightly more likely. (x+1)/(2x) I think maybe.

On the other hand, my intuition says I've done something wrong, and odd and even are coin flips. Any ideas?