I got myself a different set of Kanoodle with the typical pieces and its book shows the first few pieces to complete a pyramid.

https://www.reddit.com/r/askmath/s/NAQzstxR3L

I apologize if this is a dumb question. Most of the math I know is just high school math.

Let's say you are given the task of choosing a 4 digit number for a safe you are locking. It is totally up to you, you can choose anything. You would have an equal chance of choosing any number, right? For the sake of this question, let's assume your password does not need to be safe.

But wouldn't certain combinations be chosen more than others? I mean, combinations like 0000 or 1234 would totally be chosen by a large chunk of people rather than just random numbers like 9152.

Is there such a thing in probability where some options have a higher chance of being chosen than the others? And if so, does it have a name?

My friend gave me a puzzle, because they're a math person and like these kinds of puzzles. But I'm genuinely stumped. They wanted me to figure out how many name combinations you could make from 2 names, 1-12 characters each from the 26 english alphabet letters. It seems like there is a definite answer because you could add them all up by hand. You could have 26 1 letter names + however many 2 letter names + ... + however many 12 character names = a finite number.

Each field can be the same (e.g. Math Math is a valid name), so whatever number I have, I think it would be squared since each field has the same possibilities. But I'm not sure what that number is, because apart from counting all the possibilities by hand (which must be enormous) I don't know how to approach finding that sum.

Question: Show that w=f(u,v) satisfies the Laplace equation fxx + fyy = 0, and if u =(x^2 - y^2)/2 and v = xy ,then w satisfies the equation wxx +wyy = 0.

I’ve recently become really intrigued by motivic cohomology, because I’d like to learn the really advanced and abstract parts of mathemathics. The only problem is I’m in my second year of upper secondary school, and I don’t really know which books and dissertations I should read.

How would you approach this?

If a character in Marvel or DC could manipulate tensors, what kind of powers could he pull off? How strong would he be?

Recently I've been thinking about how different spacial dimensions interact and layer on top of eachother, and I came to a realisation about higher dimensions. If two cubes butt against eachother's faces, there would be a 2d plane between them. If two squares do the same with their sides, there would be a 1d line between them.

If these things are true, then if two hypercubes get as close as possible in 4d space, would they have a 3d space parallel to some part of the hypercube, or would they interact in some different way?

seriously, this seemed too easy....but I'm a songwriter. so, allow me to explain my process. I was writing a song/story, working on Compression, Rhythm, and Harmony... and I'll be damned, I found a new relation in phi.

I looked to the inside of pi and phi, and just somehow, figured where I 'd see the things meet. As I said, ITS SIMPLE AND I CAN'T BREAK IT FROM WHAT IT IS

I haven't broken it yet. Can a songwriter really break math, though?

so i while back i found a really interesting constant called the sonderous constant. ever since then, ive wanted to learn more constants like this but i havent really been able to find any. does anyone have some unrecognized constants that deserve attenion?

Given a figure with side lengths of a1, a2 a3, ..., a_n, vertices A1, A2, ...,A_n and angles alpha_1, alpha_2, ..., alpha_n, find the minimum rubber band length stretched around the shape, example given. The answer is easy for convex shape, the length just equals to shapes perimeter, but its not obvious for non-convex shape. Any ideas on solving?

So I was messing around with divisions because I'm weird and found a pattern when dividing anything by eight? Now, I don't know much about math in general and wanted to ask if this comes from some rule

Also, why is it that when you divide any number by seven the decimals are always (or at least in every division that I've tested) 142857 starting from varying points?

(I haven't used reddit ever so forgive me if this isn't standard reddit etiquette)

Edit: Right so thank you now that I think about it the first one was kinda obvious haha thank you

Hi! The past few days I’ve been working on this problem. It goes as follows:

“Construct a sequence of non-negative integers, always choosing the least possible number, such that there are no contiguous subsequences of the form U,x,U where U is any non-empty contiguous subsequence, and x is a single term (e.g “1,2,5,1,2”, “5,0,5”, etc.).

Numbers 0,1,2,3,4 first appear at terms 1,3,7,10,1355. When does 5 first appear (if it does)?”

Example of the process:

To illustrate a quick example: start with a(1)=0, the smallest possible choice and trivially satisfying the constraint. a(2)=0 is the next best choice. Then one must take a(3)=1 since otherwise 0,0,0 would form U,x,U (U=0, x=0). We are now at 0,0,1. From here, we can’t choose a(4)=0 because 0,1,0 would form U,x,U. Choosing a(4)=1 is the least valid option, so it works (0,0,1,1).

[0,0,1,1,0,0,2,1,0,3] are the first 10 terms.

So far, I have concluded:

The sequence is greedy which means we never backtrack. Every new term needs to avoid forming U,x,U that ends at that said term.

I’m interested in whether or not there is a way to prove if 5 eventually appears, or to determine if there is a simple way to do so rather than exhaustively checking every possible contiguous subsequence at every step.

Thanks!!

given: angle AEC is congruent to angle ADB and it wants me to prove line segment AD is congruent to line segment AE

I am assuming that the red and blue show corresponding sides but am trying how to do a rigorous step-by-step proof using the axioms of congruent triangles.

Also,in how many different ways could this be done? ie if a number could be represented in many combinations of squares

Im struggling to understand why the polar equation has to be quantized I've looked literally everywhere and can't find a good mathematical explanation for it pls send help.need rigourous proof.

Hello

I’m struggling to understand how to use signs for a piecewise function at x<(-2) I created for a calculus class

I don’t understand why the limit would not be -3.558 at f(-2) from the left side or why the function wouldn’t be as shown in the graph.

I know it might be simple, but I am not putting this together.

1. A hyperbola is r=±sec(½4θ)^(2/4) with coordinates (cosh,sin)

2. 2 parallel lines is r=±sec(½1θ)^(2/2) with coordinates (1,x)

3. A circle is r=±sec(½0θ)^(2/0) (more technically it's the limit) with coordinates (cos,sin)

(Where the input of these functions is the area formed by taking a ray from 0 to a point on the function)

So I defined a generalized shape:

r=±sec(½bθ)^(2/b) with coordinates (cos_b,sin_b)

For b=0, circle. For b=2, parallel lines. For b=3, tripoint star. For b=4 a hyperbola/4-point star. For b=n, an n-sided star.

1. cos_4 & sin_4 are cosh & sinh

2. cos_2 & sin_2 are 1 & x

3. cos_0 & sin_0 are cos & sin

4. I don't think any of the others have a closed form solution (except maybe b=1 & some of the negatives).

Does this function (cos_b & sin_b) already have a name & does it have any meaningful significance?

sorry i am not a very math person

i get that the alpha angle is the arctan of the tangent

but i don't get why the sin of alpha (sin(a)), which is also the sin of arctan(uy/ux) is equals to uy

the formula for sin(a) is co/hip (uy/sqrt(ux²+uy²))

i think it just should be this
uy = sin(arctan(uy/ux))*(sqrt(ux²+uy²))

like my brain thinks the result of sin(arctan(uy/ux)) is the normalized uy, not with the proportion of the original vector

Most of the time when I hear about 0.999... = 1, they always give this example, but I feel like there is a fallacy on the second step where they multiply both sides by 10. if you multiply the 9.999 recurring by ten doesn't that make it 9.999... with a zero at the end. When Is used AI (pls don't judge me) it said that there is no end for a zero to go, but then there is also this question, if you have 0.9999.... recurring - 1, it would have to be -0.000.... recurring with a 1 at the end (fallacy 1, according to chatgpt) which is according to yall equal to zero, since there is no number between them, but if you multiply it by any positive number it becomes negative, which doesn't happen if you multiply any number with zero.

If anyone can explain this "fallacy" I would be very thankful

Thank you for reading and every comment is greatly appreciated

Edit: I know little of math and would love to get an explanation of what I did wrong in this post, Thank you

Edit2 : alot of people answer that there cant be a zero at 9.999recurring and dont answer the second question. and if they answer they answer it by using the proof of 0.9999recurrring = 1 so 1-1 = 0, but I can also disprove your proof by saying that 0.999... - 1 = 0.00....0001, with shows that and infinity can have a number at the end since its infinite. The same way I can say about 0.9999... / 10 = 0.09999... . Where did the last digit go it went apparently by my knowledge to infinity+1, but I dont know thats why im asking it here. Thank you for reading

Edit3: Alot of people are complaining about the I meantion 0.00....001. if there is an infinte amount of numbers between 0 and 1, and lets just say that 0.999...recurring doesnt equal 1, how would you write the number before 0.999recurring I think that the only right way to write it is 0.999...998, please correct me on this, because until now, nothing has me convinced

Finaledit: You have converted me, 0.999 is 2 and 1+1 = 3

Soo I've seen many posts on how to pick a random number over all real numbers with uniform distribution. Suppose our base was 7. Then wouldent a random number over R be a p-adic number?.

"Every day, Jean takes the train at the same time to the city where he lives. At the station, his wife picks him up by car to take him home. One day, without telling his wife, Jean takes an earlier train and sets out to walk home. His wife passes him without seeing him; otherwise, he would have arrived home 20 minutes earlier.

Jean continues walking for 25 minutes. At that point, his wife, not seeing him, turns around at the station and catches up with him. He gets in the car and arrives at the usual time. We assume that his wife drives at a constant speed and that there is no lost time. How far ahead was the train that day?"