shape, congruence, similarity, transformations, properties of classes of figures, points, lines, angles
1
vote
1answer
55 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 ...
2
votes
1answer
28 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
2answers
33 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 ...
0
votes
0answers
25 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 ...
3
votes
3answers
66 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 ...
-4
votes
0answers
42 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
40 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
0answers
22 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 ...
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 ...
1
vote
4answers
30 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:
1
vote
1answer
38 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$$ft$ then what is $AD$?
I have tried to find the diamenter of the circle and the ...
4
votes
1answer
44 views
How to find area of triangle from its medians
The length of three medians of a triangle are $9$,$12$ and $15$cm.The area (in sq. cm) of the triangle is
a) $48$
b) $144$
c) $24$
d) $72$
I don't want whole solution just give me the hint how ...
3
votes
3answers
35 views
Finding side of rectangle using given information
Really simple question but I am stuck. The following information is given:
$$BD=8,\quad AB = 6,\quad ED =5,\quad EF = EC$$
and we want to find $AF$.
If we have three $90^\circ$, what does that ...
1
vote
1answer
32 views
Packing circles on a line
On today's TopCoder Single-Round Match, the following question was posed (the post-contest write-up hasn't arrived yet, and their explanations often leave much to be desired anyway, so I thought I'd ...
2
votes
3answers
34 views
Right-angled isosceles triangles
If a right-angled triangle is isosceles then the other two angles must be equal to $45^\circ$ ?
Is this always the case or are there other possible right-angled isosceles triangles?
1
vote
1answer
41 views
Find next point in ellipse given the chord length
I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse.
Given the chord (circle radius), how can I calculate the next point in ...
0
votes
1answer
33 views
triangle, vectors, proving an identity.
I'm trying to prove something but unfortunately I can't.
Let $ABC$ be a triangle and $M$ a point in $[AB]$ where $d(A,M)=d(B,M)$.Let also be
$N$ be a point in $[AC]$ where $d(A,N)=d(B,N)$.
Prove ...
0
votes
1answer
32 views
Expressing a point in two coordinate systems
Let $(O,e_1,e_2,e_3)$ and $(O',e_1',e_2',e_3')$ be two coordinate systems. Let $\overline{OO'}=2e_1-e_2+3e_3$, $e'_1=e_1-e_2+3e_3$, $e'_2=e_1+e_2+e_3$ and $e'_3=e_1-e_2-e_3$.
a) Find the coordinates ...
2
votes
0answers
40 views
Puiseux series and Resolution of Singularities
I have a very basic knowledge of algebraic geometry(no schemes!), and am trying to study the resolution of singularities.
So the Newton's method gives us a Puiseux series parametrizing the branches of ...
2
votes
1answer
80 views
How to prove this inequality $xy\sin^2C+yz\sin^2A+zx\sin^2B\le\dfrac{1}{4}$
Let $x,y,z$ is real numbers,and such that $x+y+z=1$,and in $\Delta ABC$,prove that
$$xy\sin^2C+yz\sin^2A+zx\sin^2B\le\dfrac{1}{4}$$
I think this inequality maybe use $x^2+y^2+z^2\ge ...
0
votes
1answer
14 views
Ray Disk intersection
So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
2
votes
1answer
21 views
Scale rectangles so they have same height and don't exceed a total width?
I have three rectangles of different sizes side by side.
I want to scale them all (maintaining their aspect ratio) so they have the same height and don't exceed a total width.
I know I could find ...
9
votes
0answers
109 views
+50
square cake with raisins
Alice bakes a square cake, with $n$ raisins (= points).
Bob cuts $p$ square pieces. They are axis-aligned, interior-disjoint, and each piece must contain at least $2$ raisins.
Note that a single ...
4
votes
1answer
41 views
Book on quadric surfaces with linear algebra
Most information that I can find about quadric surfaces is written from a calculus perspective - without using any matrices or vectors. However, I would like to have a reference that tells me the ...
0
votes
0answers
28 views
How do you calculate the angle of deflection of a plumb line towards a mountain?
How do you calculate the angle of deflection of plumb line being pulled down by the entire mass of earth, 5.89 x 10^24 kg and being pulled horizontally by the entire mass of mount everest, 6.399 x ...
2
votes
4answers
47 views
Relation between chords length and radius of circle
Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the ...
1
vote
1answer
33 views
Find the value of $\tan^2\alpha+\cot^2\beta$
A circle with centre o have two chords AC and BD,which are intersecting each other at P.If $\angle AOB=15^\circ$ and $\angle APB=30^\circ$,then find out value of
$$\tan^2\angle APB+\cot^2\angle COD$$
...
3
votes
1answer
52 views
Find max and min of $IJ + FE + GH$
Let $D \in \triangle ABC$. Passing through D, contruct$\, FE \parallel AB, IJ \parallel AC, GH \parallel BC$. Find max and min of IJ + FE + GH
Can this problem be solved by AM-GM ? I tried $IJ + ...
0
votes
1answer
30 views
Find position on surface of a lens
If I have a lens with coordinates UV on the lens surface where U, V are [-1, 1] and I want to find the real-world (x,y,z) coordinates of the UV point, how would I do that if I have the following ...
2
votes
3answers
122 views
On integral of a function over a simplex
Help w/the following general calculation and references would be appreciated.
Let $ABC$ be a triangle in the plane.
Then for any linear function of two variables $u$.
$$
\int_{\triangle}|\nabla ...
1
vote
1answer
54 views
Solve for an Ellipse Tangent to 2 Lines [duplicate]
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 ...
0
votes
2answers
57 views
Find the ratio of Surface area$^3$ and volume$^2$ of an sphere
IF surface are and volume of a sphere are S and V respectively,then value of $$\dfrac {S^3}{V^2} $$
a) $32$ unit;
b) $9$ unit;
c)$18$ unit ;
d)$27$ unit;
I know the formula $S=4\pi r^2$ and ...
0
votes
1answer
35 views
How can I draw a polygon from a set of angles?
In recreational mathematics, polytans are polygons formed by edge-connecting isosceles right triangles. Order-n polytans are those constructed from n such triangles. My question is this:
Given a ...
0
votes
1answer
24 views
Conformal Map from Vertical Strip to Unit Disc
I haven't found a similar question on here, though I suspect the question may be rather well-covered.
I want to find a conformal map from the vertical strip $\{z:-1<Re(z)<1\}$ onto the unit ...
0
votes
1answer
22 views
Collinearity in n dimensions
What is the best way to check if $m$ points are collinear in $n$ dimensions?
I mean I have
$p_1=(3, 4, 5, 2),\quad p_2=(6, 3, 4, 2),\quad p_3=(5, 3, 5, 6),\quad p_4=(4, 2, 7, 4)$
or
...
3
votes
3answers
40 views
area of triangle
In $\triangle ABC$ points $D,E,F$ are on the sides $AB,BC,CA$, respectively, with $AD=DB$, $CE=3BE$ and $AF=2CF$. If the area of $\triangle ABC$ is $480 cm^2$, how do we find the area of $\triangle ...
0
votes
2answers
29 views
Similar cones - volumes and lateral areas
Two similar cones have volumes 9$\pi$ and 72$\pi$. If the lateral area of the larger cone is 32$\pi$, what is the lateral area of the smaller cone?
I did the following...
$\frac {(9\pi)^3} ...
4
votes
1answer
40 views
Apples and their volumes
An apple has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the apple is the peel?
I tried
$$\frac{\text{volume}(\text{radius of 6})-\text{volume}(\text{radius ...
2
votes
1answer
25 views
Equation of third side of Triangle
A Triangle is formed by Pair of lines
$$ ax^2+2hxy+by^2=0$$ and a third side L3.Given the Orthocentre of Triangle is $$(c,d)$$, Find Equation of Third Side.
2
votes
1answer
22 views
The shortest distance between a vertex in a simplex and a non-adjacent face
Provided a simplex defined by four vertices $(v_1,v_2,v_3,v_4)$, and known edge lengths, for a given vertex $v_i$, how can I calculate the shortest distance between $v_i$ and the non-adjacent face of ...
1
vote
1answer
32 views
Are the area of a circle inscribed in a square and the area of the “spandrels” (the four corners that remain) commensurable?
And how would you demonstrate that most simply?
See the beginning of my blog post for a little more:
http://seekecho.blogspot.fr/2013/02/different-ilks.html
1
vote
2answers
50 views
Is Euclidean Geometry complete and unique
Please help me understand this concept of completeness of geometry and set me on the right path.
This is my context: From wikipedia, a formal system is complete if every tautology is also a theorem. ...
0
votes
1answer
40 views
distance between two circle's centres
Two circles of equal radius intersect at points C and D.The centres of the two circles are points A and B respectively.If their radius is 10 units,the area of triangle ABC is 40,then how do we find ...
4
votes
1answer
57 views
Geometric proof
Let the three sides of a triangle be $a,b$ and $c$. If the equation
$$a^2+b^2+c^2=ab +bc+ac$$
holds true, then the triangle is an equilateral triangle.
How do we prove this? An answer or even ...
4
votes
3answers
35 views
How to write a point on an ellipse using r and theta
We can write any point on the circle as $(r\cos\theta,r\sin\theta$), Can we do samething for the ellipse?
1
vote
3answers
44 views
How can I fold paper into 3 x 4 grid? Or prove that it can't be done?
I am trying to fold paper so that it looks like 3 x 4 grid of 12 rectangles of equal size.
Like this https://www.wolframalpha.com/input/?i=3+x+4
Its easy to get 4 rectangles. Just fold twice. But ...
1
vote
2answers
34 views
How do I find the point between two point at a specific distance (in x,y coordinates)
I am working on a programming project and have run into a problem.
I need to find a point that is on a line. For example if my line is AC and I have the coordinates for point A and C, how can I get ...
0
votes
1answer
35 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 $z$?
1
vote
0answers
30 views
Dolbeault cohomology of $S^{2n-1} \times S^1$
Let $X=S^{2n-1} \times S^1$. I have to compute $H^{(1,0)}_{\bar{\partial}}(X)$ and $H^{(0,1)}_{\bar{\partial}}(X)$. I don't know how to do this but if we use Kunnet formula we have that ...
3
votes
1answer
56 views
Could someone help me calculate the areas in this map?
Map of my book - Please click here to see it
So, I'm writing a book and I'm trying to be really detailed. Right now I'm writing a wiki of it and I want to specify the areas of continents and cities.
...
