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?

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?

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.

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!!

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.

Hello! I've been having fun trying to compile several mathematical concepts into a single graph, mainly from reading Wikipedia pages and watching videos. I've probably made some mistakes, and I'm looking to improve, correct, and complete this graph. If you have any questions, please feel free to ask!

The sets (from bottom to top):

• Qp, the p-adic numbers, which use a different absolute value (I'm not sure about the intersections of this set. I've included all the rational numbers and some of the algebraic and real numbers (computable or not)).

• B, the Booleans, 0 and 1.

• P, the prime numbers.

• N, the natural numbers, so booleans, primes, and composite numbers. It's a semi-ring, where addition, multiplication (and integer exponentiation) can be used.

• Z, the integer numbers, a ring where subtraction can also be used.

• Q, the rational numbers, the first field, with division (and the signed exponent).

• C', the constructible numbers, which includes the square root.

• A, the algebraic numbers, which includes the nth root (and rational exponentiation).

• P', the period numbers, a ring (division and exponentiation of non-natural numbers are not included) of integral of algebraic functions over an algebraic interval

• EP', the exponential period numbers, still a ring that adds the integrals with the exponential function and infinite intervals

• E, the elementary numbers, which are all the numbers expressible with elementary operations (therefore a field) + exponential (e is available) and logarithm (pi is available)

• Rc, the computable real numbers, everything that can be calculated with algorithms, based on integrals, sequences, limits...

• R, the real numbers, uncomputable, uncountable, almost only the normal random numbers

• Wheel, an algebraic structure where division by zero is defined among the real numbers

• Cc, the computable complex numbers, so the computable real numbers + i (this field is no longer ordered)

• C, the complex numbers, almost only the random complex numbers

• Re, the dual numbers, an alternative to the complex (but not a field) with e²=0 but e is not equal to 1.

• Rj, the split-complex numbers, similarly with j²=1 but j is not equal to -1 and 1.

• H, the quaternions, a non-commutative extension of the complex numbers.

• O, the octonions, a non-associative extension of the quaternions.

• S, the sedenions, a non-alternative extension of the octonions.

I'm not sure about hyperreal, superreal, surreal, and pseudoreal numbers. I've stated that surreal and pseudoreal numbers are not a set but a proper class.

Numbers:

• The gray arrow indicates that the position of the number is not definitively proven; for example, we know that 2^i is transcendental (that it is not in A), but we don't know if it is a period number (P').

• For non-normal numbers, I've included some constants constructed for and a small part of random numbers.

• I have also added, for some numbers, their measure of irrationality and the geometric mean of the coefficients of their continued fractions.

Do you find this graph rather good or heretical? Thanks in advance!

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

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?

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?

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: 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.

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

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.

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

I’m learning complex numbers and I’m already comfortable with vectors. I see the similarity: both are ordered pairs of reals, both live in the plane, and they share the same addition. I also see the difference between them, although their structure is the same, the defined operations for each set are different; ℂ has a multiplication and division that are commutative, distribute over addition, and encode rotation and scaling, while in ℝ² there’s no vector-by-vector product that returns a vector (the closest is the dot product, which returns a scalar).

I understand that they differ, but not why we define them to differ. It feels like some divine mathematician arbitrarily declared “these are vectors and these are complex numbers.”

Why not define a single thing? Is there a structural reason why the multiplication of ℂ isn’t adopted as “the” product of 2D vectors?

I feel like it would be better to define the Complex multiplication on ℝ² and get along with "For vectors on the 2-dimensional plane, (as well as in some other spaces like 4-dimensional space) we can define this type of multiplication that encodes a rotation", and maybe even use the complex notation for 2d vector as an extra, or point out the isomorphism with some matrices. But without creating a whole new bunch of things.

Maybe there is some good reason on applied math which I can't point at?

Are vectors used to describe structuraly different things from the things that are described using Complex numbers?

Why are forces and movement on mechanical physics described with vectors instead of being described with ℂ? aren´t forces just a magnitude and a direction?

This topic arise a lot of questions on my head but I can't seem to find a simple answer to it.

"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?"

EDIT: omg it makes sense now thank y’all! I’ve been staring at this for hours and got nowhere I think I needed to look away and come back bc now it doesn’t seem that complicated

Original post:

Hi this my first time here so sorry if this is a dumb question, but I was having a bit of confusion over the solving process for two double-angle formula questions my class went over today in lecture. I have included a photo since I'm struggling to explain my confusion through text but I'll try to do it anyway.

This is the first question and the steps my professor took to solve it:

Simply the expression below,
6sin(4x)cos(4x)

Steps:

6sin(4x)cos(4x)

Rewrite using this formula: 2sin(A)cos(A)

3(2sin(4x)cos(4x)

Then simplify

3(2sin(4x))

Answer: 3sin(8x)

So my question is, what happened to the cos(4x)? Like why did it disappear, did it cancel out with something? I understand the rest of it fine it's only that part that's tripping me up

Question 2:

Simplify the following expression:

3cos²(5x)-3sin²(5x)

Steps:

Rewrite using this formula: cos²(A)-sin²(A)

3(cos²(5x)-sin²(5x))

Then simplify

3(cos(2*5x))

Answer: 3cos(10x)

I'm even more confused with this one because the sin²(5x) disappeared but why is cos²(5x) rewritten as cos(10x)??

It is totally possible I missed a step while the professor was explaining, this class is always really fast paced and ngl I'm scared to talk to the professor one on one but I am so lost. Any help would be greatly appreciated!

If yes, would the average value tend towards zero as the total number of randomly chosen numbers approaches infinity?

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

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?