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

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2
votes
1answer
38 views

how to find the 8th term of a geometric sequence when you aren't given the first term [closed]

the question is asking find the 8th term of each geometric sequence with the given terms and the issue i am having is how would i know what the actual equation is when they give me a term really far ...
2
votes
1answer
17 views

Is it possible to find angles inside a shape if I am only given the slopes and lengths of the lines?

I was given a math problem listing 4 ordered pairs of points to plot. So I plotted them, found their slopes and distances. The question asks me to determine the most precise name of the quadrilateral. ...
2
votes
1answer
52 views

Intersection of two circular arcs with same center [closed]

How do you programmatically get intersection points of 2 circles given the same centers, radii, and sweep angle? The 2 circles are not exactly one whole circle. I have an equation for each circle: ...
0
votes
1answer
19 views

Find the position of a circle tangent to two other circles

Say there are 3 circles, A, centered at point a, B centered at point b, and C, centered at point c. Each has a known radius independent of the others, Ar, Br, and Cr. The positions of a and b are ...
1
vote
0answers
25 views

Why Are Fresnel Functions Used For Splines?

Why are Fresnel functions still used in the research and implementation of clothoid splines? They cannot represent curves of constant curvature, which has led to a lot of research/implementation ...
1
vote
1answer
23 views

How to prove $ABC$ is isoceles?

In Triangle $ABC$, $M$ lies on $AC$ and $N$ lies on $AB$ such that $\angle BNC = 4x$, $\angle CMB = 5x$,$\angle CBM =5x$ and $\angle NCB =6x$. Prove that triangle $ABC$ is isosceles. My attempt: ...
1
vote
1answer
34 views

How many degrees of freedom are in a flat metric and how does one count them?

I think that there are zero degrees of freedom in a flat metric, but I do not know how to count them. I know that any symmetric metric tensor has $n(n-1)/2$ degrees of freedom, where $n$ is the ...
1
vote
2answers
41 views

Find where 2 triangles intersect in 3d

I need to know when two triangles intersect in a 3D environment, given the 3 points. Any help appreciate have been stuck on this for a long time, ive been told "Step one. Get the equations of the ...
0
votes
1answer
22 views

Partion the boundary of a $n$-dimensional ball and write each partition as the graph of a $C^1$-function on a open subset of $\mathbb{R}^{n-1}$

Let $$S:=\left\{x\in\mathbb{R}^n:\left\|x\right\|_2\le r\right\}$$ How can we partition the boundary $\partial S$ of $S$ and write each partition as the graph of a continuously differentiable function ...
1
vote
1answer
35 views

Sphere - Sphere intersection cone angle

Consider the formation of a lens by intersection of two spheres. How can I calculate the cone angles formed for each spheres formed by the line connecting the centers of the spheres and the line ...
-1
votes
0answers
17 views

(Kiselev) Construction of an arc of a circle

Using only compass, construct a 1 degree arc on a circle, if a 19 degree arc of this circle is given. The first thing that is stumping me is if we can use a straight edge? In any case, I can think of ...
0
votes
0answers
22 views

connections between polar set, polar cone?

Given a set $S$, its polar cone http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone and its polar set http://en.wikipedia.org/wiki/Polar_set are defined. Could some please tell me the ...
0
votes
1answer
28 views

Calculating the volume of an oblique ellipse cone

I am trying to calculate the volume of an oblique cone that is an ellipse (rather than a circular cone). I have the following measurements Perimiter of the Ellipse (in cm) Slant Height of longer ...
3
votes
0answers
24 views

How to calculate a reduced volume?

Let's say we have an irregular 3D shape with volume=V ( we know V but we don't know its equation= F). Now I want to calculate another 3D shape which is exactly the same shape but one size smaller, ...
1
vote
2answers
32 views

Identifying compositions of reflections, and rotations in a hexagon

Let $ABCDEF$ be a regular hexagon that is oriented clockwise (so that a rotation from $A$ to $B$ to $C$ to $D$ to $E$ to $F$ is clockwise). i) Identify $R_{D,120} \circ R_{A,60}$ which are two ...
3
votes
2answers
65 views

Distance between two rectangulars

I have faced a problem, that I need to calculate a shortest distance between two rectangulars, which are on a different angles. Known parameters: length, width, angle and coordinate of center ...
3
votes
0answers
14 views

Intersection of the composition of two glide reflections

i am taking a geometry course and we are learning about isometries. I am having a hard time with glide reflections and this problem is giving me some issue, mainly because my professor usually tells ...
3
votes
3answers
63 views

How to find the area of the following triangle

I am stuck on the following problem: Let ABC be an isosceles triangle having two equal sides of length $20$ cm. and the angle between the two equal sides is $45^{\circ}$. Then I have to find ...
1
vote
1answer
14 views

Find the number of triangles formed by 2 parallel points and a non-collinear point.

There a 11 points on a plane with 5 lying on one straight line and another 5 lying on a second straight line which is parallel to the first line. The remaining point is not collinear with any two of ...
0
votes
0answers
16 views

Show if a point belongs to the area of a complex polygon

I would like to know if there is a way to know if a point belongs to the area of any polygon just by knowing the coordiantes of all the points making the boundary of the polygon , given thaht where I ...
4
votes
1answer
52 views

Can some one help me parametrize $\frac{x^4}{a^4}+\frac{y^4}{b^4}+\frac{z^4}{c^4}=1$

Given a surface $$\frac{x^4}{a^4}+\frac{y^4}{b^4}+\frac{z^4}{c^4}=1$$how can I parametrize the surface using $X(u,v).$ I tried to use $$x=a\sqrt{\cos(\theta)\sin(\phi)}$$ ...
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votes
0answers
25 views

3D vector perpendicular calculation

Three points $A(6,7,-6)$,$ B(0,0,0)$ and $C(2,6,9)$ are given which are the vertices of a cubes. Find the coordinates of another vertex not on the $ABCD$ plane. I found the answer by finding the ...
1
vote
2answers
32 views

Three circles, 5 points of intersection, prove that two circles are tangent

There are 3 circles and 5 points of intersection (point of intersection is a point where at least 2 circles meet). Prove that two circles are tangent (it means that they intersect in a single point)
0
votes
1answer
28 views

Find rectangles whose area increases by a factor of 20 when their length and width increases by k

Is there an easy way of knowing which rectangles have the same property? (length+k)(width+k) = 20(length*width)
1
vote
2answers
26 views

The height of two triangles

My textbook says the height of the following triangles ($BC$) is $37.5$ Because $$ \widehat{B_1}=\widehat{B_2}=30 \Rightarrow BD=50 \Rightarrow DC=25 \Rightarrow AC=75 $$ and since in right ...
0
votes
2answers
32 views

Volume of a region?

It is my intuition that the volume of the solid such that $0\leq x_1 \leq x_2 \ldots \leq x_n \leq T$ is $\frac{T^n}{n!}$. Can someone confirm/deny and/or supply proof? Thanks!
2
votes
2answers
28 views

How to translate a vector and then rotate by a point

I am trying to do this problem: Identify the combination formed by first translating by the vector $(2,0)$ and then rotating by $90$ degrees about $(0,0)$. but I'm a bit confused so, I ...
0
votes
1answer
19 views

Given the parallelogram solve for z [closed]

Solve for z by using the parallelogram below.
4
votes
2answers
60 views

Deriving the value of $\pi$ from a dart board

I saw this on a website and it was pretty interesting: The circle inscribed in the square has a radius of $1$ and the square has a side length of $2$. This means that the area of the circle is: ...
0
votes
1answer
33 views

integral curves of vector fields

If we have a vector field on a boundary less and compact 2-manifold, which is neither a gradient nor a harmonic, does that imply its integral curves are closed?
2
votes
1answer
49 views

3D Dodecahedron model: Construction question.

The image below is a 2D construction that, when cut-out and folded appropriately (hopefully it is intuitively clear how to cut and fold), forms a 3D dodecahedron. It works great: I've successfully ...
1
vote
1answer
27 views

What is steepness, what is flatness?

I have 3 graphs rather like $$y = \frac{1}{x}$$ and I am supposed to describe which one is steepest and which one is flattest. This is for an Econ class, so I'm not sure the terminology being used is ...
2
votes
1answer
30 views

Area of Spherical Polygon

It appears to me that after repeated applications of Girard's theorem on the area of spherical triangles that we can obtain the surface area of a spherical polygon with interior angles ...
-1
votes
2answers
39 views

A relation between area and diameter of a triangle

Let $|T|$ and $h_T$ the area and the longest side of a triangle $T$, respectively. Is there a constant $C$ (independent of the triangle) such that $|T|\leq C h_T$ ?
1
vote
0answers
93 views

Cabri 3D - Rotating a triangle

I'm given the exercise, in Cabri 3D, to rotate the triangle T around the axis AB and lead it via the triangle To to the triangle T'. I tried to rotate the triangle T around a fixed point and then ...
0
votes
1answer
59 views

What is the probability that a random line meet both of the opposite side of a square? [closed]

If it is known that a random line meets a side of a given square, show that the probability that it also meets the opposite side is p = sqrt2— 1.
5
votes
2answers
221 views

Insert squares into square [on hold]

Let $ABCD$ be a square, $AB=2a$ Is it possible to insert two disjoint squares, both of side $a$ into $ABCD$?
0
votes
0answers
15 views

Convex pyramid with same pyramid volume formula

Areas $ A_1,A_2 $ of parallel planes are of $n$ sided polygons spaced distance/ height $H$ apart. How should generators of a solid be defined so that solid volume can continue to be calculated by the ...
-2
votes
0answers
8 views

Definition of collinear line segments in a 2D plane.

Let AB and CD be two straight line segments in a 2D plane. Can I say that AB and CD are collinear line segments when they lie along the same (infinite) straight line?
1
vote
0answers
27 views

Area of circles on a wall

If you are painting a wall that is 10 ft by 12ft blue with gray polka dots on it, and the polka dots are spaced their diameter's distance away from each other at the shortest distance, how much paint ...
0
votes
1answer
39 views

a question about how to parametrize a surface in $R^3$

Given a surface $$x^4/a^4+y^4/b^4+z^4/c^4=1$$,how can I parametrize the surface using X(u,v). I tried to use $x=a\sqrt{cos(\theta)sin(\phi)}$,$y=b\sqrt{cos(\theta)sin(\phi)}$,and ...
1
vote
1answer
23 views

Formula for Points of a Projection

Given a projection from the point $(-1,1)$ that maps $y = 2x$ onto $ y = 2x - 3$. How do I find a formula for where the points of $y = 2x$ map on $ y = 2x - 3$? Any assistance would be appreciated.
1
vote
0answers
28 views

Can I generate a skewed ellipse tangent to two points?

I'm trying to write a python script to generate a trailing edge (TE) for an airfoil with no TE. Basically want to make a smooth round-off nose profile to the right, the closure line should come out ...
1
vote
0answers
21 views

Isomorphism of projective general linear group and the general linear group modulo its center

I want to prove that $PGL(n,q)\cong GL(n,q)/Z(GL(n,q))$. (This is actually the usual definition for PGL if we study the matter algebraically but geometrically, this only comes as a theorem, as I have ...
0
votes
2answers
35 views

Find line equation using another line's equation and the angle

So, I have the problem described exactly as in the figure below. I want to find the equation for the green line given the data described in the figure. I know that $$\tan(\text{angle of elevation for ...
5
votes
1answer
42 views

Fitting a circle

Given a figure like , how can I determine the radius of the circle with middlepoint H analytically? CDFE is a square with sides 6/5, with E and F being points on the circles with radii 2.
1
vote
1answer
37 views

Find the image of circular points by fitting conics

According to Single Axis Geometry by Fitting Conics by Jiang et al., one can compute the image of the circular points in a picture from conics which are the images of circles. Fit two conics to ...
3
votes
2answers
112 views

Proper axiomatization of Euclidean Geometry that Euclid would approve of

It is relatively common knowledge that Euclid's axiomatization is not sufficient to prove all the things that Euclid wants to, and that there are other axiomatizations out there that strengthen ...
0
votes
1answer
38 views

Flex a square into a circle, and prove…

Let points $A$, $B$, $C$, and $D$ be the vertices on a square. Let $\overline{CD}$'s midpoint be $E$. Flex the square into a circle (so they'll have equal perimeter/circumference), and translate the ...
2
votes
2answers
63 views

Proving a Simple Fact about Slopes of Lines

The following problem is a detail from a proof I wrote recently -- a detail that I left unproven, and would like to prove. Let there be three points $a$, $b$, and $c = \frac{a+b}{2}$, with $a<b$. ...