Tagged Questions

shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles

2answers
30 views

How to find length when viewing at some angle?

I have a question on angles. I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some ...
1answer
37 views

How to find length of a rectangular tile when viewing at some angle [duplicate]

I have a question on angles. I have a rectangular tile. when looking straight I can find the width of the tile, but how do I find the apparent width when I see the same rectangular tile at some ...
1answer
26 views

Prove triangles with same perimeter and point of tangency of excircle and nine-point circle.

In triangle ABC let X be the point of tangency of the excircle opposite A with side BC. (A) Prove that the segment AX divides triangle ABC into two triangles, each having the same perimeter. (B) Prove ...
1answer
28 views

calculate rotation from 2 3d lines

I am trying to extract the transformation of a segment described by two 3d points $(a_0,b_0)$ into the transformed points $(a_1,b_1)$. I have been able to calculate the translation, and I am assuming ...
1answer
29 views

How do I prove that the triangle must be obtuse?

Suppose you are given a triangle where the center of the nine-point circle lies on the circumcircle of the triangle. It is obvious that the triangle is obtuse, but how can you formally prove that the ...
1answer
26 views

How to sketch the graph of $\varphi(X)=d(X,A)+d(X,B)$ when $A$ and $B$ are not given?

$A,B$ are points in an axis, disposed in this order. Sketch the graph of the following function: $$\varphi(X)=d(X,A)+d(X,B)$$ $d(A,B)$ is the distance from point $A$ to point $B$. I'm ...
1answer
19 views

Question about the dimension of the intersection of two subspaces of a vector space $V$.

Let $M, N$ be two subspaces of a vector space $V$ with dimension $k$. Suppose that $\dim M=m$, $\dim N =n$. It is said that $\dim M \cap N \geq m+n-k$. Suppose that $M, N$ are two parallel planes in ...
1answer
29 views

The best softwares to understand the intersections of the 3D objects in the Euclidean space

What is the best software (Easy to follow and clear graphics) to draw the intersections between two spheres, Two spheres and a pyramid, for example. The centre and the radius of the spheres are given ...
2answers
42 views

If the diagonals of a trapezoid are congruent, then the trapezoid is isosceles.

Thanks in advance to anyone who can help me out on this. I'm currently a junior in high school taking and doing well my school's honors pre-calc class, but of all of the math I've ever learned, proofs ...
3answers
60 views

Distance between two antennas

I am trying to find out the formula to calculate how high antennas need to be for Line of Sight (LoS) propagation. I found: d = 3.57sqrt(h) also ...
3answers
61 views

Permutations and Cross-ratios

Pick four distinct numbers, list all 24 permutations, and compute the cross-ratio of each permutation. Show that at most six numbers have occurred, given by the cross-ratio group \$y, \frac{1}{y}, 1-y, ...
2answers
45 views

Constructing Points

Given that you have two lines intersecting at the origin "0", with the unit "1" marked on each line, and "2" marked on the second line, clearly show how you would construct the point (2+1), the point ...
2answers
48 views

Showing that f cannot be a linear fractional transformation

Let $f(x) = \frac{x^2}{x+1}$. Show that f cannot be a linear fractional transformation. (Hint: do not try to argue that f cannot be put into the form of $\frac{ax+b}{cx+d}$).
0answers
29 views

Generating Linear Fractional Transformations

Let $f(x)$ be a linear fractional transformation of your choosing, as long as $a, b, c, d \neq 0$ and $ad-bc \neq 0$. i) Express $f(x)$ as a composition of generating transformations. ii) Pick four ...
1answer
50 views

Limits of the Minkowski distance as related to the generalized mean

Given that the Minkowski distance is $$d(X=(x_1,...,x_n),Y=(y_1,...,y_n))=(\sum_{i=1}^n|x_i−y_i|^p)^{1/p}$$ I understand that $$\lim_{p\to\infty}d(X,Y)=\max_{i=1}^n|x_i-y_i|$$ ...
1answer
19 views

Given two lat/long/altitude points, how do I find the north/east/up vector between the two points?

I have two lat/long/altitude points $(\phi_1,\lambda_1,h_1)$ and $(\phi_2,\lambda_2,h_2)$. I wanted to find the distances in the east and north directions (up is fairly obvious, I think?) between ...
0answers
21 views

maximum length of a scaled vector in a triangle (simplex)

Given a triangle (or, in general, a simplex) $T$ and a vector $\vec{s}$, I'd like to compute the quantity $$\max\{|x-y|: x,y\in T, x-y = \alpha \vec{s}, \alpha\in\mathbb{R}\}$$ i.e., the maximum ...
1answer
84 views

contest problem in geometry

Suppose the inscribed circle of $\triangle A_1A_2A_3$ touches the sides $A_2A_3, A_3A_1, A_1A_2$ at $T_1,T_2,T_3$. From the midpoints $M_1,M_2,M_3$ of $A_2A_3,A_3A_1,A_1A_2$, draw lines perpendicular ...
3answers
59 views

Finding mass of a sphere whose density is given

I want to find the mass of a sphere of radius $a$ whose density at a point is proportional to the distance of a point from a plane passing through a diameter of a sphere
1answer
22 views

equation of a plane passing through a diameter of a sphere

I want to find the equation of plane passing through a diameter of a sphere, For simplicity let us assume that origin,$(0,0,1)$ and $(0,0,-1)$ are on a diameter, then the points lie on the plane ...
0answers
23 views

Imaginary line passing through non-collinear points in R3.

I have come to a problem where n points are provided in 3-Dimensional plane. I need a imaginary line which can be assumed that it is passing through these points.
3answers
64 views

Equation of Cone vs Elliptic Paraboloid

I can't understand why $$\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2} \tag{*}$$ corresponds to an elliptic paraboloid and $$\frac{z^2}{c^2} = \frac{x^2}{a^2} + \frac{y^2}{b^2} \tag{**}$$ to a cone, ...
0answers
43 views

Good textbooks on Non-Euclidean Geometry?

I'm currently taking a class called Foundations of Geometry. We started with the stereographic projection and carried onward through fractional linear transformations, and now we are working with the ...
1answer
30 views

Problem with finding the intersection point between a line and triangle

I have a mathematical problem that I'm trying to solve, but the equations I have derived don't give the correct output when utilised on concrete problems. However, I can't figure out what the problem ...
2answers
55 views

Looking for a (nonlinear) map from n-dimensional cube to an n-dimensional simplex

I am looking for a (nonlinear) map from n-dimensional cube to an n-dimensional simplex; to make it simple, assume the following figure which is showing a sample transformation for the case when $n=2$. ...
2answers
63 views

A part of an I.M.O problem

Let $a$ be the base of a triangle and $a+b$ be its perimeter. Using the fact that area of triangle is maximum when the other two sides are equal, prove that among all quadrilaterals with fixed ...
2answers
43 views

Calculate new positon of rectangle corners based on angle.

I am trying to make a re-sizable touch view with rotation in android. I re-size rectangle successfully. You can find code here It has 4 corners. You can re-size that rectangle by dragging one of ...
0answers
57 views

Does this graph have a name?

Does graph shown below from the paper Dissection Graphs of Planar Point Sets by P. Erdos, L. Lovasz, A. Simmons, and E.G. Straus have a name? Does it come from a family of related graphs?
1answer
41 views

Length of DNA strand

The DNA molecule has a double helix structure. The radius of each helix is approximately $10$ angstroms ($1$ angstrom $=10^{-8}$cm). Each helix goes up by approximately $34$ angstroms every ...
0answers
28 views

A rectangular prism has the surface area of 300 square inches. what whole number dimensions will give the prism the greatest volume. [duplicate]

it is a tough geometrical algebra problem It is tough and involves geometry and algebra. thank you
1answer
220 views

Maximizing the volume of a rectangular prism

A rectangular prism has a surface area of $300$ square inches. What whole number dimensions give the prism the greatest volume? This is a math olympiad problem. It involves the volume and surface ...
3answers
36 views

Problem with determining cylinder height

Here is a question that I have, but I have no idea where to do go from here. Here is the question: The vase company designs a new vase that is shaped like a cylinder on the bottom with a cone on ...
1answer
18 views

How to I calculate a second plot point given the first point and the slope?

Is there a formula to calculate the second point in a segment given a starting point, segment length, and slope? Thanks
3answers
40 views

Please help me find a formula to find the 3rd point in a right triangle

I'm trying to figure out how to plot a 3rd point on a graph Given the following line segments and angles Is there a formula for the 3rd point? Note: This image is just for an example. The base ...
1answer
50 views

If I have three points on a circle, how do I calculate other points on the same circle?

I have circle which I know intersects the x axis at -11.5 and 11.5. It intersects the Y axis at 1. How can I calculate the (positive) Y value for any X value between -11.5 and 11.5? This is to ...
1answer
24 views

finding an equation through these two points in upper half plane

I have to find an equation going through $(-1,y)$ and $(1,y)$. The equation my book uses is $x^2+y^2+ax=b$. So I get two equations when I plug in the two points. I get $1+y^2-a=b$ and $1+y^2+a=b$ ...
1answer
27 views

Please help me to find an equation to find the 3rd point in an arc.

Long story short, I want to animate the rotation of an object that's based off a circle. Given the center point of the circle, the radius, and one of the points in the arc, is it possible to find the ...
3answers
63 views

Parametric equation of an ellipse

How do I show that the parametric equations $$x(t) = \sin(t+a)$$ $$y(t) = \sin(t+b)$$ define an ellipse? I tried graphing it and I'm certain it is a rotated ellipse. My first idea is to write it ...
0answers
61 views

Geometrical Inequality

Let $ABCD$ be a quadrilateral on the unit circle, and the diagonals $AC$ and $BD$ intersects at $E$. If the shortest height of the triangle $ACD$ equals the radius of the incircle of the triangle ...
2answers
121 views

A concise distance problem

A falsely simple Euclidian geometry problem: Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$. What is the set of possible $\|AC\|$ ? I'm after a concise answer, ...
5answers
138 views

Does $e$ have a geometric representation? [duplicate]

Just like $\pi$ is the ratio of a circle's circumference to its diameter? I know that the tangent line to the function $e^x$ has a slope of $e^x$ at that point, but is there some other geometric ...
1answer
71 views

circle of inversion

Determine the equation of the circle reflection of the line $x = 2$ if the circle of reflection is $x^2 + y^2 + 2x = 0$ which in standard form is $(x+1)^2+y^2=1$ where $radius=1$ and center is ...
1answer
49 views

Center of circle that has two points on its circumference and a known tangent

I've found a related question, which helped me get started on this. I can get it to work for the example on the question, but I'm running into an issue when the tangent is not y = 0. Other question ...
1answer
21 views

Condition for a quadrilateral to be tangential

Define a quadrilateral to be tangential iff all four of its internal angle bisectors meet a a single point. Prove the following: A quadrilateral is tangential if and only if three of of its ...
1answer
22 views

Pascal's theorem in geometry

We denote $P= WX \cap YZ$ to mean point $P$ is the intersection of lines $WX$ and $YZ$. The problem is about pascal's theorem: Let $ABCD$ be a cyclic quadrilateral. Let the tangent lines at A and at ...
1answer
36 views

Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points?

According to Pick's Theorem, the size of an area $A$ can be calculated by the sum of the interior lattice points located in the polygon $i$ and the number of lattice points on the boundary placed on ...
1answer
80 views

help on a geometry problem

$ABCD$ is a convex quadrilaterial such that $AC=BD$. $AC$ and $BD$ intersect at $E$ and $\angle AEB=66^{\circ}$. $F$ and $G$ are the midpoints of $AD$ and $BC$, respectively. $FG$ intersects $AC$ ...
2answers
18 views

What's the geometric interpretation of a semidenifite matrix smaller than identity matrix?

What's the geometric interpretation of a semidenifite matrix in terms of eigenvalues/eigenvectors with the condition: $$0 \preceq W \preceq I$$
4answers
111 views

What's the best 3D angular co-ordinate system for working with smartfone apps

This is very much an applied maths question. I'm having trouble with Euler angles in the context of smartphone apps. I've been working with Android, but I would guess that the same problem arises ...
1answer
55 views

Inscribing equilateral triangle in rectangle

Problem: What is the area of the largest equilateral triangle that can be inscribed in a rectangle with sides $10$ and $11$? (The problem comes from an old high school math contest. I believe it's ...
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