# Questions tagged [applications]

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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### Decoding Every Top 100 Voting Ever

I need expert help on the math behind the following voting mechanism, any comment towards solutions are greatly appreciated! -- A country is holding a poll to determine the top 100 restaurants out ...
2k views

### Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...
21 views

### Why/How bow's method works?

We can find compression and tension forces of bars using graphical method(bow's method/bow's notation). Why/How does it work? Or How you can prove it?
59 views

### Robustly estimating exponential growth?

Say we have a model $$f(x) = c_1e^{-c_2x}$$ We know we have some noise, but we don't know where it is, if inside exponential or added outside and we don't know the distribution. How can we robustly ...
8k views

### Uses of quadratic reciprocity theorem

I want to motivate the quadratic reciprocity theorem, which at first glance does not look too important to justify it being one of Gauss' favorites. So far I can think of two uses that are basic ...
3k views

### Elementary proof of the Prime Number Theorem - Need?

Although I am very much new to "Analytic Number Theory", there are some non mathematical questions which puzzle me. First of all, why was G.H.Hardy so keen to have an elementary proof of the Prime ...
64 views

### Real life applications of a circle? (Conics)

for my Math 2U assignment, we have to discuss real life applications of different conic sections. However, apart from the wheel, I cannot find or think of any other real life applications of the ...
46 views

### Has the rigour of real analysis shown some unexpected truths about real life that would have otherwise not be discovered?

It is a common question, "what is the use of real analysis", and the answer is usually "it adds rigour to our mathematical tools and machinery to make sure that they work without just saying they do". ...
54 views

### Is gaussian elimination “used”?

According to the book Linear algebra and its applications by Strang, "(The) good method is Gaussian Elimination. This is the algorithm that is constantly used to solve large systems of equations". Is ...
48 views

### Mathematics of war references

I have an upcoming talk in on data science. Now a ways such topics have been hijacked by talks on the use of machine learning. Deviating from the trend, I want to focus of core advancement of ...
2k views

### Mix two colors in LAB color space

I have two colors in LAB color space, for example: blue: 32.303, 79.197, -107.864 (hex code: #0000ff) yellow: 97.138, -21.556, ...
27 views

### “Gaps in the Mats” problem

Problem Background* The mat at your karate dojo composed of 160 square interlocking foam tiles. Along each edge of each tile, there are has five "teeth" (10cm long) and five spaces-for-teeth (again ...
5k views

### Why does the Elo rating system work?

The Elo rating system is used to rank players in games such as chess. I can find plenty of explanations online of how to compute someone's Elo rating, how to actually crunch the numbers in practice, ...
12 views

### What is considered to be a Heap’s law?

I’m not sure if this is more physics question than mathematics but anyways. Something is usually said to follow Heap’s law if it is given as a function $V(n)=K n^b$, where $b$ and $K$ are constants (...
32 views

### How to convert an instantaneous mortality rate to a weekly mortality rate

I want to convert an instantaneous mortality rate that is reported per year (actual value = $0.58y^{-1}$) into a weekly mortality rate. This answer gives the formula as $j=(1+i)^{1/12}-1$ where $j$ ...
5k views

### Physical interpretation of Laplace transforms

One may define the derivative of $f$ at $x$ as $\lim\limits_{h\to0}\cdots\cdots\cdots$ etc., and show that that has certain properties, but it also has a "physical" interpretation: it is an ...
844 views

### Center of mass of a trick sphere-cone intersection

B is the solid region occupying the space situated inside the sphere of radius R centered at the origin and above the cone of equation $z = \sqrt{x^2 + y^2}$. The B density is proportional to the ...
96 views

### Is there anything significant about the cross-quarter days, in terms of a sinusoid?

As the Earth goes around the sun, the length of the day changes, and certain cultures have celebrations or observances centered around these changes, illustrated in this graph. The red dots, the ...
7k views

### What is a simple, physical situation where complex numbers emerge naturally? [duplicate]

I'm trying to teach middle schoolers about the emergence of complex numbers and I want to motivate this organically. By this, I mean some sort of real world problem that people were trying to solve ...
349 views

### Cryptocurrency Math

I'm looking for any relevant books/articles on the maths of cryptocurrency transactions. Also open to any resources that may have some cryptocurrency transactions but not it may not be the main bite. ...
62 views

### Were the wagers in the June 3, 2019 Final Jeopardy! round rationale?

The long-running U.S. television program Jeopardy! is a trivia question-and-answer (or answer-and-question) game show, involving three players competing to be the fastest to correctly answer questions,...
41 views

### What are the use cases of the Dirichlet energy in computer vision?

I am reading a paper, in the context of computer vision, that mentions the "famous" Dirichlet energy. I am not familiar with this Dirichlet energy, but apparently we can minimise it. What are specific ...
24 views

### searching for function composed of s(x) + x with reasonably efficient inverse

To model my data, i need a function that resembles $f(x) = s(x) + x$ with $f : \mathbb{R} \rightarrow \mathbb{R}$, where $s(x)$ is a sigmoid-like function with co-domain $(0,1)$. So if we look at the ...
267 views

### Represent a Toeplitz matrix in an array

I need to represent a $n \times n$ Toeplitz matrix in a $2n - 1$ array. I need to create a function that takes a pair $(i,j)$ and returns the value in the $2n - 1$ array. I am having a difficult time ...
2k views

### What is the use of Calculus? [closed]

I know this may seem like a really broad question, but I will narrow it down. I really want to know the purpose of some of the things my teacher is emphasizing in my calc class. For example why it ...