For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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0
votes
3answers
33 views

Dividing line segments with ratios vs. fractions [on hold]

I know that 2:3 is actually 2/3. So when you split a line segment by a ratio, you would add 2 and 3 to get a fraction of 2/5 that will be used to solve the problem. I can't really seem to find much ...
1
vote
0answers
18 views

System of quadratic equations for a tetrahedron

I know the dimensions of the base of a tetrahedron and the angles between the non base sides at the apex. I want to know the lengths of the three non base sides. Let the base's corner points be $A, ...
2
votes
2answers
18 views

How to find perpendicular point of a vector to another vector 2d

Given the axis x-y and some random points to the vectors AB and CD, how can i find out where will the point D lie when the vector CD(dashed line) is perpendicular to AB. For example if point A has ...
0
votes
1answer
15 views

Why does the focus point distances of an ellipse sum up to the length of the major axis diameter

Why does the distances from the focus points of an ellipse to arbitrary point in the ellipse sum up to the length of the diameter of the ellipse in the major axis? In other words, how to prove: I ...
0
votes
1answer
12 views

Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
2
votes
1answer
15 views

Weighted average of multiple points

Let's say I have a triangle whose three corners are $$(x_1,y_1),(x_2,y_2),(x_3,y_3).$$ I have a weight assigned to each one as a percentage, so the first point might be $75\%$, the second $15\%$ and ...
1
vote
1answer
34 views

Lines joining origin to points of intersection of two conics

If the lines joining origin and point of intersection of curves $$ax^2+2hxy+by^2+2gx=0$$ and $$a_1x^2+2h_1xy+b_1y^2+2g_1x=0$$ are mutually perpendicular, then prove that $$g(a_1+b_1)=g_1(a+b)$$ How ...
1
vote
3answers
37 views

Meanings of Sine, Cosine, Tangent

Whenever I have a question dealing with sine, cosine, and tangent, my teacher always says to use a calculator. I would like to know how you would solve these without just using a calculator, that way ...
1
vote
0answers
12 views

Trig equation that fits the plot points (octagonal pyramid)

I'm looking for an equation that satisfies these conditions: Input 90 degrees, result is 90 degrees Input 45 degrees, result is 60 degrees Input 0 degrees, result is 45 degrees For an input value ...
4
votes
0answers
30 views

Is the non-existence of a general quintic formula related to the impossibility of constructing the geometric median for five points?

In particular, in the Computation section of in the Wikipedia page for geometric median, there is this statement: ...but no such formula is known for the geometric median, and it has been shown ...
1
vote
1answer
20 views

How could I calculate the local size of an object given its distance and actual size?

Lets say I take a picture of a sign. I know that sign is 20ft (width), 10ft height. I'm standing 40 feet away. If I were to take a picture, how could I calculate how wide and how high the sign is in ...
0
votes
1answer
21 views

Find the Equation of BC

$\Delta ABC$ with vertex $A(1,2)$ has equations of internal angle bisectors of $\angle B$ and $\angle C$ as $x-y-1=0$ and $2x+y-9=0$ Respectively. Find the Equation of $BC$ My approach: Solving for ...
1
vote
4answers
21 views

Find depth of a half-filled parabolic cross-section

Given a cross-section of an object that is parabolic in shape, how do you find the depth of the object when it is "half full". A full example given in an exam: A long trough whose cross-section ...
1
vote
0answers
68 views

Why does base*height work?

I want to rigorously prove the idea that Base*Height=Area works (I do realise there are shapes which do not satisfy this equation). I think I can see why it works for integer values, but I want ...
-10
votes
1answer
50 views

What's the lenght? [on hold]

Imagine a roll of sheet outer radius R and inner radius r and the thickness dx , what's the length? I'm interested to see how many different solution or approach to this problem exists !
0
votes
0answers
21 views

How do I compute corners of geodesic rectangle?

I have the center of a rectangle as a latitude and longitude as well as the length of the sides in meters and the orientation in radians. How can I compute the ...
2
votes
0answers
40 views

Geometry - formula for angles in isosceles triangle

EDITED: new picture, less confusion. Please view the picture above. It is an isosceles triangle It is mirror symmetric, all circles are EQUAL in radius. Let the green and purple angles be P and ...
1
vote
1answer
26 views

Find rigid transform from coordinates of the same points in different reference frames

Given two* 3-dimensional points $p_1$ and $p_2$ expressed in different reference frames $A$ and $B$, find the rigid transform (rotation and translation) between frames $A$ and $B$. The answer to this ...
1
vote
1answer
18 views

Axis dimensions of oval around inscribed rectangle

I have a rectangle of known width and height. This rectangle is inscribed in an oval. So, to be clear, the corners of the rectangle are just touching the oval, making the oval as small as possible ...
0
votes
0answers
11 views

Time of flight for a projectile with stated initial velocity and size at various distances [migrated]

I've been mooching round the internet looking for an answer to this one and can't find a ready resource, hence the question. In short, I'm trying to discover the flight time of a shotgun pellet at ...
0
votes
1answer
13 views

Medians of a triangle and the sides of the triangle relationship [duplicate]

Suppose the medians of a triangle are 5,12 and 13 units, find the sides of the triangle. I understand that the medians meet and form centroid. But I am uncomfortable to apply this to this problem
0
votes
1answer
18 views

I'm looking for two euclidean polytopes such that their cartesian product is no longer a euclidean polytope.

I'm looking for two euclidean convex polytopes such that their cartesian product is no longer a euclidean convex polytope. Does such a thing exist? Note here by convex polytope I mean the set $ K ...
2
votes
0answers
30 views

Ratio of angles of a right triangle

P.S: I only want a hint,not the whole solution. BdMO 2009 Problem 5 Secondary In triangle ABC, $\angle A = 90$. M is the midpoint of BC. Choose D on AC such that AD = AM. The circumcircles ...
1
vote
2answers
25 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
0
votes
2answers
52 views

How to find the intersection points of lines that are normal to two curves?

Let I have two curves, \begin{gather} f(x)=\frac{x^3}{4}+1 \\ g(x)=\frac{(x-\tfrac{1}{2})^3}{7}+\tfrac{1}{2} \end{gather} There are zero or more lines that are normal to both curves. In other words, ...
-4
votes
2answers
92 views

What is the area of a 12cm square? [on hold]

I am working through a maths revision sheet based on measurement and I have come across a question that simply states, what is the area of a 12cm square?
0
votes
1answer
25 views

Minimal number of points to define a rotated ellipse?

What is the minimal number of points $N$ to uniquely define the semi-major axis $a$, the semi-minor axis $b$ and the rotation angle $\omega$ of an ellipse whose the center is known/fixed (this is ...
3
votes
2answers
83 views

The relationship between two definitions of star-shaped domain

There are two definitions of star-shaped domain. One is given in wikipedia as follows. Def1: A set $S$ in the Euclidean space $\mathbb{R}^n$ is called a star domain (or star-convex set, star-shaped ...
-1
votes
1answer
40 views

How to get the third point coordinates in isosceles triangle?

Isosceles triangle $ABC$ $AB = AC = d_1$ $BC = d_2$ $A = (x_1, y_1)$ $B = (x_2, y_2)$ $C = (x_3, y_3)$ $\angle BAC = \phi$ $\angle ABC =\angle ACB = \theta$ I want an equation for $x_3$ and $y_3$ ...
1
vote
0answers
23 views

How prove that $(DB+BC)^2=AD^2+AC^2$ in convex quadrilateral?

Let ABCD be a convex quadrilateral,and write $\alpha =\angle DAB,\beta =\angle ADB,\gamma =\angle ACB,\delta =\angle DBC , \epsilon =\angle DBA. $ Assuming that $\alpha <\frac{\pi}{2},\beta +\gamma ...
11
votes
5answers
226 views

Unit circle is divided into $n$ equal pieces, what is the least value of the perimeters of the $n$ parts?

A unit disk is divided into $n$ equal pieces, that is, each piece has area $\dfrac\pi n$. equal "pieces" means equal area Let $l_1, l_2,\dotsc,l_n$ be the perimeters of the $n$ parts, ...
0
votes
1answer
30 views

Show that every imaging f with certain properties is a group

Let $f:\hat{C}\to\hat{C} $ a bijection with the property to sent lines an circles to lines and circles. Show that f is a group with operation the composition of functions (images) (whom obviously ...
2
votes
1answer
26 views

Is it possible that the fact the number of inflection points is zero changes in some different coordinate system?

Let $L$ be a line segment in the $3D$ Euclidean space. And Let $L_{xy}$ and $L_{xz}$ be the projections of $L$ onto the $XY$ and $XZ$ planes, respectively. Assume both of $L_{xy}$ and $L_{xz}$ have no ...
0
votes
1answer
38 views

? Confocal ellipses and hyperbolas cover whole Euclidean plane

I need a proof that we can use confocal ellipses and hyperbolas, with given foci and given perpendicular bisector of the the line segment between the foci and given pair of rays prolonging the line ...
2
votes
1answer
45 views

Help with simple rotation on an x,y plane

I'm a programmer, with too little background in mathematics, and I am currently faced with the challenge of rotating an object on a 2 axis plane. Something that is hopefully quite easy for you guys. ...
0
votes
0answers
21 views

Angle of a complicated triangle [duplicate]

what is the magnitude of $\angle DEB$? I tried this puzzle with angle sum property of triangle. I could not arrive at the solution
0
votes
1answer
38 views

Number of triangles formed by all chords between $n$ points on a circle

We have $n$ point on circumference of a circle. We draw all chords between this points. No three chords are concurrent. How many triangles exist that their apexes could be on circumference of ...
0
votes
1answer
14 views

About the interior ball condition of a convex set with C^1 boundary

Let $\Omega$ an open bounded and convex domain in $R^n$. Suppose that the boundary of this set is $C^1$. Then $\Omega$ satisfies the interior ball condition for all boundary points? Intuitively ...
1
vote
1answer
41 views

problem about length of perpendicular chords

Question $AB$ is chord of circle $O$,points $D$ and $E$ are chosen on $AB$ in a way that $AD=BE$.prove two chords that are perpendicular to $AB$ and pass $D$ and $E$ points are equal.(prove $LK=MN$) ...
1
vote
1answer
40 views

How to find an angle in range(0, 360) between 2 vectors?

I know that the common approach in order to find an angle is to calculate the dot product between 2 vectors and then calculate arcus cos of it. But in this solution I can get an angle only in the ...
7
votes
2answers
95 views

General method to “naturally interpolate” to a complex map?

Given a region of the complex plane and a map $z \to f(z)$, is there a general way to "naturally interpolate" the point $z$ to $f(z)$ in such a way that the movement follows a "natural" smooth path ...
0
votes
0answers
32 views

Is the cartesian product of two polytopes again a polytope?

Given two polytopes $P_1, P_2$ then define the graph on $P_1 \times P_2$ as follows: $[(a,b),(x,y)]$ is an edge in $P_1 \times P_2$ iff $a=x$ and $[b,y]$ is an edge in $P_2$ or $b=y$ and $[a,x]$ is ...
0
votes
0answers
9 views

krull dimension of a direct limit of commutative rings

What can be said about the Krull dimension of a direct limit of non noetherian rings commutative rings with unit with constant Krull dimension?
-4
votes
0answers
43 views

Zeros of vectorial field [on hold]

Given a $M$ manifold in ${\mathbb R}^n$ and $X:M\rightarrow TM$ a vectorial field such that $\pi\circ X=Id$ where $\pi:TM\rightarrow M$ (projection to $M$). One zero of $X$ is such that ...
15
votes
5answers
640 views

Is there a way to calculate the area of this intersection of four disks without using an integral?

Is there anyway to calculate this area without using integral ?
11
votes
3answers
240 views

Difficult Recurrence

I am trying to solve a Sangaku problem. The blue circles have radii one. The goal is to find the total area of all the other circles (the three sequences of circles repeat ad infinitum). I have ...
4
votes
1answer
38 views

Geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts

What's the geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts? For example, a skew-symmetric matrix on its own can be interpreted as an infinitesimal rotation. As ...
1
vote
1answer
29 views

A bounded domain can be considered as a compact manifold?

A bounded domain $\Omega$ with smooth boundary $\Gamma$ can be considered as a compact connect Riemannian manifold?
2
votes
1answer
29 views

Finding equation of line with given slope

Find the distances of the point (1,2) from a straight line. The slope is given to be 5 and the line passes through the intersection point of the lines $x+2y = 5$ and $x - 3y = 7$ Obviously I could ...
0
votes
1answer
14 views

Triangle Theorem relating the shortest and longest distance from any arbitrary point inside

I recall somewhere there was a relationship such that given a triangle T and a point A: if A is inside of T, then the sum of the longest distance from A to any point on a side of T, plus the shortest ...