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Geometrical Interpretation of Risk Ratio (RR)

Can anyone suggest any book or article on the topic "Geometrical Interpretation of Risk Ratio (RR)" ?
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22 views

What can/do mixed second-order partial derivatives represent?

What I know from basic calculus: The first derivative of a function $f:\mathbb{R}\to\mathbb{R}$ gives an indication of the function's behavior (namely, how the value of $f(x)$ changes as $x$ changes). ...
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What does Dini continuity mean?

What does Dini continuity (the integral condition) mean visually? Description of Dini contuity: https://en.wikipedia.org/wiki/Dini_continuity
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0answers
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Why does the Hilbert transform produce the Hilbert envelope?

The Hilbert transform is often described as an improper integral. It can be also characterized as a convolution between two functions. But why is it these descriptions that produce the so called ...
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1answer
89 views

$A^tA-AA^t$ in Mathematical Physics

In very different contexts of mathematical physics (rigid body mechanics, fluidodynamics, general relativity, quantum field theory,...) I have come across the following expression: $$ A^tA-AA^t, $$ ...
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1answer
58 views

What is the Geometric interpretation of $i^i$?

We know that $i^i$ is real. But how to explain it geometrically maybe in terms of rotation. like we can explain geometrically multiplication of two complex numbers and so on. Can someone show me a ...
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1answer
27 views

Geometrical condition for the intersection of two circles

On the plane, one can give a simple condition for the intersection of two circles $\mathcal{C}_1(O_1,r_1),\mathcal{C}_2(O_2,r_2)$ : they intersect iff $|r_1-r_2|\le|O_1O_2|\le r_1+r_2$. Likewise, can ...
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0answers
36 views

Open sets in $\mathbb C$ and open sets in $\hat{\mathbb C}$

I usually have a lot of trouble with complex variable when it comes to the geometric representation of $\hat{\mathbb C}$ and what happens in there. I have the next exercise and from quick look at it I ...
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1answer
79 views

Is there a nice meaning to the geometric triple product?

Using geometric algebra, I can easily find the geometric tripleproduct of three vectors $a,b,c \in \mathbb{R}^3$ to be $$abc = a \left(b \cdot c \right) - b \left( c \cdot a \right) + c \left( a ...
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2answers
73 views

Geometric Interpretation of Fractional Derivatives

I was looking for a geometrical interpretations of fractional derivatives and fractional integrals. I would be glad to see any kind of intuitive and preferably visual interpretation of the objects ...
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8 views

Interception Solid

Could someone draw for me (in $\Bbb R^3$, $x,y,z$ axes) the resultant solid of the interception of $x^2+y^2 \le 1$ and $y^2+z^2 \le 1$? I'm getting a little tired of thinking about the solid but can't ...
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How do I put this into a linear equation?

I really don't know what I would do first. I moved $x$ to the other side of the equal sign to make it $2y = 12 + x$ and then I was going to divide it by $2,$ but i realized you can't divide $x$ by ...
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1answer
64 views

Geometric interpretation of 2D-Translation's Matrix representation

I just learned the trick of writing a translation of a 2-dimensional real vector as a matrix multiplication in a 3-dimensional space - wikipedia explains it here. Basically it shows: $$ ...
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1answer
58 views

Geometric interpretation of determinant of a system of homogenous linear equations

What is the geometric interpretation of the determinant of a matrix representing a system of homogenous linear equations? We know that iff the determinant is equal to zero the system has a ...
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2answers
71 views

Are there any formulas or identities that involves $\pi$ but have no obvious trigonometric interpretation?

Every formula that involves $\pi$ has an underlying trigonometric interpretation but it is not usually obvious. I wonder if there are any formula like the Gaussian integral ...
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38 views

Find the geometric interpretation of general solution

Here are the linear equation: $$2x+z=0$$ $$-x+3y+z=0$$ $$-x+y+z=0$$ I have found that the general solution is, $$t \begin{bmatrix} \frac{-1}2\\ \frac{-1}2 \\ 1 \\ ...
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105 views

physical interpretation or practical meaning of a distance

How can I find/understand the physical explanation or practical meaning of a distance? For example Euclidean distance is the shortest path between two points, how about for other distances?
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10answers
439 views

Why is it that $\int_a^b \int_c^d f(x)g(y)\,dy\,dx=\int_a^b f(x)\,dx \int_c^d g(y)\,dy$?

The title sums it up. It's simple to prove, but I'm wondering if there is a geometric interpretation?
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Interpretation of the complement $S_5 \setminus D_6'$.

On account of a homework question $$ \text{does there exist an injective homomorphism } D_6 \to S_5 \text{ ?}$$ which I solved positively, I raised the question $$ \text{what does the complement ...
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100 views

Rotation of Matrices and their interpretation

Given are now two matrices and I have to discuss what the given functions are doing (geometrically). Maybe you can revise/add the following: given are the matrices $ A = \begin{pmatrix} \cos(a) ...
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2answers
81 views

Interpretation of vector line integrals

I recently came across two types of line integrals which I had not previously come across before and am unsure as to what their interpretation would be: Integrating a scalar field with vector line ...
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1answer
26 views

Showing for $f,g:\mathbb{R}\rightarrow\mathbb{R}$ that for $M>0, |f(x)|\le M|g(x)|$ for $x>x_0$

Showing for $f,g:\mathbb{R}\rightarrow\mathbb{R}$ that for $M>0, |f(x)|\le M|g(x)|$ for $x>x_0$. This is a repost of a question that is probably too long to ever get an answer (I feel compelled ...
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0answers
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Odly phrased big-oh question, have I done what is required? (because it's not really big-oh, it's more graph sketching)

I've encountered these before, but never phrased or defined as follows, I'd like to know if I've done whatever the question wants to draw attention to (if it didn't want to draw attention to ...
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3answers
206 views

Geometry of the dual numbers

A dual number is a number of the form $a+b\varepsilon$, where $a,b \in \mathbb{R}$ and $\varepsilon$ is a nonreal number with the property $\varepsilon^2=0$. Dual numbers are in some ways similar to ...
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Can something like $\text{Hom}(V,K)$ be visualised?

I have no trouble visualising vector spaces like $\Bbb R^3$ and (e.g.) a subspace of dimension $2$, which would just be a plane through the origin of a $3$-D space, but I'm having trouble visualising ...
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1answer
84 views

Interpretation of Linear Algebra and superposition

I have been told and have seen that knowing Linear Algebra is foundational in pursuing advanced mathematics. After dealing with it enough I have gotten "used to it" (I still need a lot more practice!) ...
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1answer
1k views

Do the BAC-CAB identity for triple vector product have some intepretation?

As in the title, I was wondering if the formula: $$a\times (b\times c)=b(a\cdot c)-c(a \cdot b)$$ for $\mathbb R ^3$ cross product has some geometrical interpretation. I've recently seen a proof (from ...
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2answers
74 views

expected value of random variables

Take two random variables $X=a+bX_0$ and $Y=c+dY_0$, and define $T=X-Y=\mu+\sigma Z$ where $\mu$ is the mean of $T$, $\sigma$ its standard deviation and $Z$ is a standardized random variable with mean ...
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2answers
179 views

$i^{th}$ root(s) of unity

If we define $S:=\{z\in\mathbb{C}:z^n=1\}$ (i.e. the $n^{th}$ roots of unity), then $|S|=n$ (i.e. we have $n$ of them). We can even go as far as to say: $$S=\{z_k:k\in\mathbb{N}\cap[1,n]\}=\{e^{2\pi ...
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1answer
127 views

Sorgenfrey line topology

For every $x\in\mathbb R$ we have $\mathcal{B}(x):=\{[x,z): z>x\}$ as the sorgenfrey line. First I want to show that there is topology $\tau$ defined on $\mathbb R$, i.e I have to show that ...
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Geometric Interpretation for Definite Integrals with $\pi$ in the result [duplicate]

What is the geometric interpretation for the following integral? What is a nice geometric interpretation for the following integral (possibly in relationship to a circle) that emphasizes why we get ...