shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
0
votes
1answer
129 views
Is this valid parametric equation to create control points for a helix in 3D space?
Is this a valid way to compute new points that are on a helix and if not what is it wrong?
The Cartesian coordinates of each new helix control point could be described by the following ...
2
votes
1answer
48 views
Prove $\sin \alpha+\sin \beta+\sin \gamma \geq\sin 2\alpha+\sin 2\beta+\sin 2\gamma $
Prove that $\sin \alpha+\sin \beta+\sin \gamma \geq\sin 2\alpha+\sin 2\beta+\sin 2\gamma $ where $\alpha$ $,\beta$ $,\gamma$ are the angles of a triangle
2
votes
2answers
81 views
Ratio of areas of similar triangles given SS
What is the ratio $ A_I:A_{II} $ ?
I know that the given angles and common angle prove the triangles are similar. Using proportionality, I found the length of the middle lengthed side of ...
3
votes
0answers
30 views
Find min of $IA + IB + IC +ID$ in tetrahedron $ABCD$
Let the point $I$ in tetrahedron $ABCD$. Find $\min\{IA + IB + IC + ID\}$.
I can't solve this problem, even in the case ABCD regular. Please help
1
vote
1answer
29 views
Circle Packing: Unsolved Problem in Geometry?
Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
0
votes
1answer
22 views
Find the bases of a Non Isosceles Trapezoid by the median and diagonal [closed]
One of the diagonals of a non-isosceles trapezoid splits its median into two parts of $3$, $5$ and $2$ cm. Find the length of the trapezoid's bases.
3
votes
2answers
26 views
Rotation of a point in 3d space
I'm trying to rotate a point around a single axis of a 3D system.
Given $P=\begin{pmatrix}
101 \\
102 \\
103
\end{pmatrix}
$,
And the rotation matrix formula for rotation around the X axis only, I ...
3
votes
3answers
63 views
Right triangles with integer sides
Most of you know these triples:
$3: 4 :5$
$5: 12 :13$
$8: 15 :17$
$7: 24 :25$
$9: 40 :41$
More generally we can construct such triangles such as
$$2x:x^2-1:x^2+1$$
My question is why one of ...
0
votes
1answer
46 views
Property of bisectors of right triangle
In triangle $ABC$ $\angle C=90^\circ$, $AA'$ and $BB'$ are angle bisectors intersecting at $I$ ($A'\in BC$, $B'\in AC$). What would be the easiest way to prove that projection of $I$ onto $AB$ lies in ...
3
votes
2answers
36 views
Physical representation of volume to surface area
I was looking at this XKCD what-if question (the gas mileage part), and started to wonder about the concept of unit cancellation. If we have a shape and try to figure out the ratio between the volume ...
2
votes
0answers
15 views
Determine direction of minimum overlap of convex polygons
Given two convex polygons $P$ and $Q$ what is the minimum intersection polygon $A=P\cap Q'$ where $Q'$ is the polygon $Q$ offset by a vector $\overline r$ of fixed length?
Put another way, what is ...
-1
votes
0answers
34 views
Distance on the surface of a sphere
Given a sphere which radius is r.
There are two red points on the sphere. Given the location of the two points in spherical coordinate system.
If the surface distance between a point and a red point ...
2
votes
2answers
253 views
0
votes
2answers
30 views
Ray-Lens Intersection
So imagine that I have a ray parameterized as $\vec{R} = \vec{O} + t\vec{D}$, where $\vec{O}$ = origin, $t$ = parameter and $\vec{D}$ = direction vector.
I also have a spherical lens with aperture ...
1
vote
1answer
32 views
Using Semi-circle find side of triangle
The figure below above shown a bicycle path. If semicircular portion $ABC$ is $100$ $\pi$ and $CD$ is $100$$ft$ then what is $AD$?
I have tried to find the diamenter of the circle and the ...
2
votes
1answer
25 views
How to Find the Center of a Parallelogram
I want to find the center of a parallelogram in order to use it in my java program. I have four coordinates of the parallelogram and I want to find the center coordinate of the parallelogram. It seems ...
0
votes
0answers
24 views
How to introduce perpendicular or congruence of angles in affine space
$n$-dimensional affine point-vector space is a pair $\mathbb A^n = \langle \mathbb A, V^n \rangle$, where $\mathbb A$ is an arbitrary set, which elements are called points of affine space, $V^n$ is an ...
0
votes
2answers
320 views
3-D geometry : three vertices of a ||gm ABCD is (3,-1,2), (1,2,-4) & (-1,1,2). Find the coordinate of the fourth vertex.
The question is
Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1,1,2). Find the coordinate of the fourth vertex.
To get the answer I tried the distance formula, equated ...
-4
votes
0answers
38 views
Find ebook A.V. Pogorelov, “Foundations of geometry”. [closed]
Can you help me find ebook : A.V. Pogorelov, "Foundations of geometry" , Noordhoff (1966).
Or book write about axoxiom systems Pogorelov in Euclidean geometry.
0
votes
0answers
38 views
How can I eliminate duplicate set elements?
Given the set of eight angles A={0,45,90,135,180,225,270,315}, if we want to draw all possible graphs that have k vertices, where each vertex must have an exterior angle chosen from A, we need to draw ...
2
votes
1answer
198 views
Change of coordinate system on a sphere
This might take a while to explain, so bear with me:
I've got a perfect sphere. I've set up an arbitrary longitude/latitude ("angle") coordinate system on it (imagine an equator around the middle, ...
0
votes
1answer
19 views
Maximal square covering
Let X be a shape in 2-dimensional space.
Define a square covering of X as a set of axis-aligned squares, whose union exactly equals X.
Note that some shapes don't have a finite square covering, for ...
0
votes
1answer
27 views
General equation of an ellipse in 3D space with respect to cylindrical coordinate systems
The regular ellipse formula in 2D is $x^2/a^2 + y^2/b^2 = 1$ but how can it be transformed into a 3D formula including the parameter of $r, \theta$ and $z$?
4
votes
3answers
2k views
Calculating a Point that lies on an Ellipse given an Angle
I need to find a point (A on this diagram) given the center point of the ellipse as well as an angle. I've been melting my brain all day (as well as searching through questions here) testing out ...
2
votes
0answers
20 views
Minimal surface representation from a 3D contour
I have a set of 3D points defining a 3D contour, as shown below. The points in this contour lie in their best-fit plane and I want to obtain a 3D triangular mesh representation of the surface inside ...
7
votes
1answer
154 views
combinatorial geometry: covering a square
I'm stuck with this problem. can anyone help me?
A finite collection of squares has total area 4. show that they can be arranged to cover a square of side 1.
1
vote
4answers
25 views
Simple geometry/trigonometry question
How to find the X coordinate of the red point if i know it's Y coordinate and the angle? Let's say the Y is 40 and the angle is 30 degrees:
4
votes
1answer
41 views
How to find area of triangle from its medians
The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is
a) $48$
b) $144$
c) $24$
d) $72$
I don't want whole solution just give me the hint how ...
1
vote
1answer
124 views
Geometry - optimal 2D mesh between X expendable points
Say you have X points on a plane.
If you connect two points, you form a line. Connecting three points forms a triangle.
A line cannot cross a line, and a smaller triangle cannot be created inside a ...
1
vote
2answers
93 views
+100
On integral of a function over a simplex
Help w/the following general calculation and references would be appreciated.
Let $ABC$ be a triangle in the plane.
Then for any linear function of two variables $u$.
$$
\int_{\triangle}|\nabla ...
5
votes
0answers
53 views
square cake with raisins
Alice bakes a square cake, with $n$ raisins (= points).
Bob cuts $p$ square pieces. They are axis-aligned, interior-disjoint, and each piece must contain at least $2$ raisins.
Note that a single ...
3
votes
3answers
34 views
Finding side of rectangle using given information
Really simple question but I am stuck. The following information is given:
$$BD=8,\quad AB = 6,\quad ED =5,\quad EF = EC$$
and we want to find $AF$.
If we have three $90^\circ$, what does that ...
32
votes
5answers
6k views
+50
Why is Pi equal to 3.14159…?
Wait before you dismiss this as a crank question :)
A friend of mine teaches school kids, and the book she uses states something to the following effect:
If you divide the circumference of any ...
1
vote
1answer
30 views
Packing circles on a line
On today's TopCoder Single-Round Match, the following question was posed (the post-contest write-up hasn't arrived yet, and their explanations often leave much to be desired anyway, so I thought I'd ...
2
votes
3answers
68 views
Geometry - Equilateral triangle covered with five circles
I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
1
vote
1answer
38 views
Find next point in ellipse given the chord length
I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse.
Given the chord (circle radius), how can I calculate the next point in ...
0
votes
1answer
106 views
How Total Station Works Mathematically?
I am working on some avr programming for a robot which can understand elevation of an object in distance for now that object is a mirror , i wonder how total station cameras works i mean mathematical ...
0
votes
1answer
32 views
triangle, vectors, proving an identity.
I'm trying to prove something but unfortunately I can't.
Let $ABC$ be a triangle and $M$ a point in $[AB]$ where $d(A,M)=d(B,M)$.Let also be
$N$ be a point in $[AC]$ where $d(A,N)=d(B,N)$.
Prove ...
2
votes
1answer
78 views
How to prove this inequality $xy\sin^2C+yz\sin^2A+zx\sin^2B\le\dfrac{1}{4}$
Let $x,y,z$ is real numbers,and such that $x+y+z=1$,and in $\Delta ABC$,prove that
$$xy\sin^2C+yz\sin^2A+zx\sin^2B\le\dfrac{1}{4}$$
I think this inequality maybe use $x^2+y^2+z^2\ge ...
2
votes
3answers
32 views
Right-angled isosceles triangles
If a right-angled triangle is isosceles then the other two angles must be equal to $45^\circ$ ?
Is this always the case or are there other possible right-angled isosceles triangles?
157
votes
13answers
11k views
4
votes
1answer
45 views
Find max and min of $IJ + FE + GH$
Let $D \in \triangle ABC$. Passing through D, contruct$\, FE \parallel AB, IJ \parallel AC, GH \parallel BC$. Find max and min of IJ + FE + GH
Can this problem be solved by AM-GM ? I tried $IJ + ...
7
votes
1answer
658 views
Simple proof for Snell's law of refraction
Snell's law of refraction can be derived from Fermat's principle
that light travels paths that minimize the time using simple
calculus. Since Snell's law only involves sines I wonder whether
this ...
0
votes
1answer
25 views
Expressing a point in two coordinate systems
Let $(O,e_1,e_2,e_3)$ and $(O',e_1',e_2',e_3')$ be two coordinate systems. Let $\overline{OO'}=2e_1-e_2+3e_3$, $e'_1=e_1-e_2+3e_3$, $e'_2=e_1+e_2+e_3$ and $e'_3=e_1-e_2-e_3$.
a) Find the coordinates ...
2
votes
0answers
38 views
Puiseux series and Resolution of Singularities
I have a very basic knowledge of algebraic geometry(no schemes!), and am trying to study the resolution of singularities.
So the Newton's method gives us a Puiseux series parametrizing the branches of ...
0
votes
1answer
12 views
Ray Disk intersection
So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
1
vote
1answer
50 views
Solve for an Ellipse Tangent to 2 Lines
I'm trying to automate creation of a curve in PowerPoint.
Here's an image of what I'm working towards:
I'm trying to show a diagram of a rocket trajectory from a launch site on Earth to a circular ...
2
votes
1answer
21 views
Scale rectangles so they have same height and don't exceed a total width?
I have three rectangles of different sizes side by side.
I want to scale them all (maintaining their aspect ratio) so they have the same height and don't exceed a total width.
I know I could find ...
4
votes
1answer
35 views
Book on quadric surfaces with linear algebra
Most information that I can find about quadric surfaces is written from a calculus perspective - without using any matrices or vectors. However, I would like to have a reference that tells me the ...
0
votes
0answers
28 views
How do you calculate the angle of deflection of a plumb line towards a mountain?
How do you calculate the angle of deflection of plumb line being pulled down by the entire mass of earth, 5.89 x 10^24 kg and being pulled horizontally by the entire mass of mount everest, 6.399 x ...
