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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5
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5answers
726 views

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 ...
24
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5answers
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 ...
0
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0answers
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?
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3answers
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 ...
41
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7answers
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 ...
14
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2answers
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 ...
1
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1answer
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 ...
1
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0answers
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". ...
2
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1answer
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 ...
0
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1answer
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 ...
2
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3answers
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, ...
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0answers
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 ...
19
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4answers
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, ...
0
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0answers
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 (...
2
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1answer
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 $j$ ...
31
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1answer
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 ...
1
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1answer
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 ...
1
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0answers
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 ...
44
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17answers
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 ...
4
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0answers
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. ...
2
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1answer
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,...
3
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1answer
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 ...
0
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2answers
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 ...
1
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1answer
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 ...
8
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10answers
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 ...
29
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10answers
43k views

Real world uses of hyperbolic trigonometric functions

I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples of their uses ...
2
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1answer
52 views

Real life application of Cyclic group [closed]

The encryption in Caesar cipher given by: $E_k(P)\equiv P+k\,(\mathrm{mod}\,26)$, where $P$ is the plain text and $k$ is the shift key. and The decryption in Caesar cipher given by: $D_k(C)\equiv C-k\...
3
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2answers
111 views

Partial Differentiation of an equation using implicit differentiation confusion

I wanted to ask a question about implicit differentiation in partial differentiation. When I was at school, I remember partial differentiation as something like this: When you have a function ...
2
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3answers
148 views

How did Carina (in Pirates of the Caribbean $5$) determine the longitude with chronometer?

At first, let me quote some dialogues from Pirates of the Caribbean $5$: Dead Men Tell No Tales. In a scene when she wants to purchase a chronometer, she has accused that she is a witch, but she ...
3
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0answers
90 views

What are practical examples of Toeplitz matrices?

A Toeplitz matrix is one in which each descending diagonal from left to right is constant. Given that structure, matrix operations are sometimes much faster. Where are Toeplitz matrices likely to ...
0
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1answer
35 views

Areas of Applied Combinatorics

I love combinatorics, but do not really want to do pure math exclusively. I like the format of pure math (that is the theorem-proof-theorem-proof format), but would also like what to do research that ...
39
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18answers
41k views

What is an example of real application of cubic equations?

I didn't yet encounter to a case that need to be solved by cubic equations (degree three) ! May you give me some information about the branches of science or criterion deal with such nature ?
10
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5answers
3k views

What is Cramer's rule used for?

Cramer's rule appears in introductory linear algebra courses without comments on its utility. It is a flaw in our system of pedagogy that one learns answers to questions of this kind in courses only ...
2
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3answers
27 views

Finding numerical values to an equation describing a hyperplane or a plane (any software suggestion?)

The following equation $$0.27a+0.1b+0.13c=70$$ can admit many solution. Is there any software/methods I can use so that I can have a large list of all the possible numerical solutions to this equation?...
0
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1answer
1k views

How can I write the radius equation for the disk method if the axis of revolution intersects the area between the curves

A specific example would be revolving the area between $x^2-5$ and $5x$ below the $x$-axis about $y=-2$ PS - in general, I am assuming that revolving about any other horizontal or vertical line ...
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0answers
11 views

Using the law of conservation of Energy for a collision under gravity.(applied maths)

One end of a light elastic string of natural length l passing through a small smooth ring of mass m is attached to a point O of a ceiling. A particle P of mass M attached to the other end of the ...
1
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2answers
49 views

What are some practical usages of computing volume in $n$ dimensions?

I am not sure if this is really a mathematical problem, but I know how to find volume of say a sphere in n dimensions, but after coming to realize how to do this, i just don't get what would be the ...
1
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0answers
12 views

Finding the optimum parameters for volumetric swept 3D display application utilizing planetary gear system

Imagine a planetary gear system as below: There are two curved screens attached to a shaft of the planet (little purple gear). The curves are logarithmic spirals. So they are rotating with the ...
1
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1answer
50 views

What would be the explicit formula of a “dictionary” function / relation?

What would be the explicit formula of a " dictionary" function / relation that would put in the "dictionary order" all the words of a natural language ( having an alphabet)? I think that one of the ...
0
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1answer
71 views

Where is the usefulness of Fourier Transform I was promised? [closed]

Before I started my PDE course I heard about Fourier Transform and how useful it is (waves, heat problem, etc) but I recently finished it and all we did is solve some PDE problems where we had to ...
4
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2answers
269 views

Real-world applications of fields, rings and groups in linear algebra.

Real-world applications of fields, rings and groups in linear algebra. A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
3
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3answers
95 views

Applications of chemical reaction networks

I have recently read a bit on chemical reaction network theory. I was wondering whether the mathematical concepts have cross-field applications like neural networks. For example, can I apply chemical ...
0
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0answers
32 views

Physical interpretation of Dirichlet energy for a membrane.

In the following model of a membrane with a mass particle in it, why does the integral represents the elastic energy of the system? Let $\Omega$ be an open connected region (the membrane) in $\Re^2$, ...
0
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1answer
43 views

Examples of applying Dirichlet's approximation.

I've seen many examples of Dirichlet's approximation being proven , or other questions regarding to the theory of the approximation on this site and others but I would like to see a concrete example ...
2
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0answers
35 views

Real world application of finding all simple paths on a graph

I am currently designing a general purpose graph database. Recently I have started to consider supporting the "find all simple paths between two nodes" operation on the graph. However while there are ...
0
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0answers
17 views

Impact of individual parts to the whole when measuring yearly performance

Suppose I have a scenario where I want to compare the performances of two different time periods, but I want to break down exactly what caused the difference in performance. I have performance of ...
0
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2answers
25 views

Norml, Application of derivatives

If $x+4y =14$ is normal to the curve $y^2=αx^3 - β$ at $(2,3)$, then the value of $α+β$ is? I equated the slope of the normal with the value of $-dx/dy$ and found $α=2$, how do I find $β$?
10
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4answers
219 views

“Class” of functions whose inverse, where defined, is the same “class”

Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for. Anyway, details. I'm asking specifically about real-valued functions on the real ...
0
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0answers
37 views

Integral transform with reciprocal complex exponential functions?

I tried answering a question that ended up with an expression $$\mathcal F\left\{e^{\left(\frac{2\pi j} {t}\right)}\right\}$$ Now this function we know from famous identity is $$e^{ai} = \cos(a)+i\...
1
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1answer
51 views

Find the interval in which $f(x)$ increases and decreases.

Let $f(x) = 2x^3 -9x^2 + 12 x + 6$ so $f'(x) = 6x^2-18x + 12 = 6 (x-1)(x-2)$ I need the intervals in which $f(x)$ strictly increases, $f'(x)>0$ when $x <1$ and $x>2$ and thus $f(x)$ ...