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
0answers
14 views

What would be simple way of calculating the area of the visible parts of a 3D PieChart's slice?

I have created a 3D Pie Chart able to be rotated. -> http://plnkr.co/edit/QIYu8sJUWPmxcby1ky9l?p=preview I did it to demonstrate how the visual perception of data in a Pie Chart can be distorted ...
7
votes
0answers
27 views

A curious triangle inequality

Let $ABC$ be a triangle. Pick a point $P$ inside the triangle. How would you show that \begin{equation} |PA|+|PB|+|PC|+\min\{|PA|,|PB|,|PC|\}\leq |AB|+|BC|+|CA|. \end{equation}
-1
votes
1answer
41 views

prove that the quadrilateral $ABCD$ is a square

Given $ABCD$ a quadrilateral such that $AB\parallel CD$ and $\angle ACD=45^0, \angle A=90^0, \angle D=90^0 $ Need to prove that $ABCD$ is a square. I tried to use circles but it didn't help. Any ...
2
votes
0answers
19 views

Proof of Bernoulli's' result on a construction to divide any triangle into four equal parts with two perpendicular lines.

I have been reading about Jacob Bernoulli and came across this particular contribution of his. Although I have tried my best to search proofs of this result I have had no success so far. Probably this ...
1
vote
2answers
32 views

Determining the position of a perpendicular line segment connecting two parallel lines that is equidistant from 2 points

I was given this problem and I can't seem to think of a solution. Here is a possibly helpful graphic: Given two parallel lines (representing the banks of a river) and two arbitrary points $A$ ...
0
votes
1answer
7 views

$N$ - Dimensional Solid of Revolution.

Ok, so if you take a line, or a group of lines, and rotate them $360$ degrees along their axis, you'll get a $3$-dimensional solid. Is it possible to take a $3$-dimensional figure and rotate it ...
0
votes
1answer
24 views

Find the length as a function of $r_1,r_2$

We are given two mutually tangent circles in the plane, with radii $r_1,r_2$. A line intersects these circles in four points, determining three segments of equal length. Find this length as a ...
1
vote
0answers
16 views

Intersection of a surface and a line.

I have a surface ($H$) that passes every corner points(one coordinate gets its maximum $1$ while others $0$), such as $(1,0,...,0), (0,1,0,...,0),....,(0,...,1).$ H is characterized by ...
1
vote
1answer
14 views

Signed angle difference without conditions

I've got two angles in $0 \leqslant a < 360$ and I need to find the signed difference between them which should be $-180 < \Delta < 180$. Is there a way to calculate the difference with ...
2
votes
0answers
37 views

Ratios of the major axes of ellipses inscribed in a triangle

I recently came across a question that went something like this: In a triangle with vertices (0,0), (6,0), (2,4) an ellipse is inscribed such that it has the largest area. Now it is dilated, that is ...
3
votes
3answers
60 views

What's the equation for a rectircle? (Perfect rounded-corner rectangle without stretching on only one dim)

The equation for a rounded square seems to be: $x^4 + y^4 = 1$ You can make the radii smaller by increasing (over the even integers) the exponents in the equation. Here's a picture: Wolfram Alpha ...
0
votes
0answers
31 views

Synthetic geometry , angles.I need some ideas

Let $ABC$ be a triangle such that $m(\measuredangle ACB)>30$ and $M$ in the interior of the triangle with $m(\measuredangle BMA)=120, m(\measuredangle BCM)=30$. Let$\{ D\} = AM\cap BC$ and $P \in ...
0
votes
1answer
29 views

Is the Locus circle?

Locus of points such that sum of it's distances of them from four fixed points remains constant? Is the locus circle? I was not able to solve it as there were four radicals. Is it a theorem?
1
vote
1answer
18 views

Distance between a point $X$ and a line $2x-y = 1$

I am asked to state a condition for a point $X$ such that the point $X$ is a distance of 10 units from the line $2x-y = 1$, and then find the Cartesian equation of the set of all points $X$ that are a ...
1
vote
4answers
62 views

How Many Times The Clock Hands Make an angle Theta?

You might have encountered such a question where $\theta=90^o$ but this a little different and is causing a little problem. I approached this problem in the following matter and solved for $\theta= ...
1
vote
2answers
30 views

Area of piece of paper folded around straight line of orientation $\theta$

Imagine drawing a straight line $l$ through the center of a square piece of paper with area $1$. Now fold the paper along that line. Q: What is the function for the area covered by the folded ...
2
votes
3answers
33 views

How to find position of point that is x unit distant from AB line segment and y unit distant from BC line segment?

I am trying to calculate coordinates of point P, which is x units distant from AB line segment and y units distant from BC line segment. Edit: I am trying to write code for general solution. As ...
1
vote
2answers
26 views

Question on geometry related to Trapezium and Isosceles Triangle

In figure $AD\perp DE$ and $BE\perp ED$.$C$ is mid point of $AB$.How to prove that $$CD=CE$$
1
vote
1answer
34 views

How to find another solution for two cone intersection?

Lets say we have two cones and they intersect: $$ \sqrt{(x-a_1)^2 + (y-a_2)^2} + a_3 = \sqrt{(x-b_1)^2+(y-b_2)^2} + b_3 $$ And we know one solution $x_1, y_1$ for this intersection. Is there any ...
0
votes
0answers
11 views

Property of all k-dimesional shapes

A close friend showed me an intuitive pattern that given a k-dimensional convex polytope P, if one doubles every sidelength to generate a $P'$ it is possible to fit $2^k$ copies of $P$ within the ...
0
votes
2answers
24 views

find the lenght of segment in a skew quatrilateral

Let $ABCD$ be rectangle so that $|AB| = x$ and $|BC| = y$. Suppose we fold the rectangle along the diagonal $BD$ so that the planes $ABD$ and $BCD$ will be perpendicular. What is the lenght of $|AC|$ ...
1
vote
0answers
21 views

given skew lines $l$ and $m$ find the geometric locus

Suppose we have two skew lines $l$ and $m$. I want to find the geometric locus of points $P$ for which there is not line passing trough $P$ intersecting $l$ and $m$. I know the locus of points should ...
-1
votes
1answer
24 views

Let $O$ be the center of the circle circumscribed around a triangle $ABC$. Does $C$ belong to the plane where the points $A$, $B$ and $O$ belong? [on hold]

Let $O$ be the center of the circle circumscribed around a triangle $ABC$. Does $C$ belong to the plane where the points $A$, $B$ and $O$ belong?
4
votes
3answers
280 views

Why is the surface area of a sphere not given by this formula?

If we consider the equation of a circle: $$x^2+y^2=R^2$$ Then I propose that the volume of half of a sphere of radius $R$ is given by the summation of the circumferences of the circles between the ...
0
votes
0answers
21 views

Concurrence of lines through triangle midpoints [duplicate]

Suppose that points $A, B, C$ form a triangle and that $A'$ $\in$ $l_{BC}$ and $B'$ $\in$ $l_{AC}$ and $C'$ $\in$ $l_{AB}$ are such that the lines $l_{AA'}$, $l_{BB'}$, $l_{CC'}$ are concurrent at G. ...
1
vote
1answer
27 views

concentration of volume of hypersphere

I am reading about features of volume of hyperballs, where I see two theorems, Most of the volume of the d-dimensional ball of radius r is contained in an annulus of width $O(r/d)$ near the ...
1
vote
0answers
36 views

Concurrence through a triangle

Suppose that points A, B, C form a triangle and that A' $\in$ $l_{BC}$ and B' $\in$ $l_{AC}$ and C' $\in$ $l_{AB}$ are such that the lines $l_{AA'}$, $l_{BB'}$, $l_{CC'}$ are concurrent at G. ...
1
vote
1answer
19 views

Calculate most parallel vector

Let's suppose I have a vector $\vec{a}$ and arbitrary many vectors (in my example two: $\vec{b}$ and $\vec{c}$), which all have a common starting point P. Now I want to find out which of these vectors ...
2
votes
1answer
68 views

Would you confirm this as a proof to the Pythagorean theorem?

I'm new in mathematics, and trying to build my way up starting by doing simple tasks. My current one is proving the Pythagorean theorem without looking it up. This photo contains my current "proof" ...
1
vote
2answers
50 views

Areas of triangles in hexagon

A hexagon $ABCDEF$ with parallel opposite sides is given. Prove that $[ACE]=[BDF].$ (here $[]$ denotes area of triangle) Since the sides are parallel does that mean that it is equiangular as ...
12
votes
7answers
1k views

Length of a Chord of a circle

I was wondering about the possible values that the length of a chord of a circle can take. The Length of a chord is always greater than or equal to 0 and smaller ...
0
votes
2answers
28 views

Geometry-||gm proof

$ABCD$ is a parallelogram in which $P$ and $Q$ are the mid points of the sides $AD$ and $BC$ respectively. If $BP$ & $QD$ intersect the diagonal $AC$ at $X$ and $Y$ respectively then prove that ...
-4
votes
1answer
26 views

Find both the diagonals with area and side given [on hold]

Side of rhombus $= 65$ cm Area of rhombus $= 1024$ cm$^2$ Find the diagonals of the rhombus.
0
votes
1answer
33 views

Rotation addition with quaternions

My task is: "Describe rotation $S \circ R$ by axis and angle, where $R$ is rotation around $(0,1,1)$ by 90 degrees, and $S$ is rotation around $(1,-1,0)$ by 90 degrees." I should use quaternion ...
0
votes
0answers
25 views

Prove that $x+y \tan {\frac{(\alpha + \beta)}{2}}=0$ [on hold]

The line joining $A(a\cos{\alpha},b\sin{\alpha})$ and $B(a\cos{\beta},b\sin{\beta})$ is produced to the point $M(x,y)$ such that $AM: BM=b:a$; prove that $x+y \tan {\frac{(\alpha + \beta)}{2}}=0$ ...
0
votes
1answer
34 views

If the coordinates of the vertices $B$ and $D$ are $(7,3)$ and $(2,6)$ respectively, find the coordinates of the vertices $A$ and $C$.

The sides of the rectangle $ABCD$ are parallel to the co-ordinate axes. If the coordinates of the vertices $B$ and $D$ are $(7,3)$ and $(2,6)$ respectively, find the coordinates of the vertices $A$ ...
0
votes
0answers
13 views

How to visualize the product of two segments lengths? [duplicate]

So there seems to be easy ways to visualize addition. If three points a, b, and c are on the same straight line respectively, we can say that the sum of the lengths of ...
2
votes
5answers
68 views

How limiting/ heavy is the “triangle inequality” assumption?

Suppose a theorem proves something about a family of distance measures, with this the triangle inequality assumption. How limiting this assumption is in reality? What are some real-world examples of ...
0
votes
0answers
13 views

Translate and Rotate mesh

I have a mesh constituted of some vertices in 3d space, let's call them $(x_1,y_1,z_1),(x_2,y_2,z_2),\cdots,(x_n,y_n,z_n)$. The mesh's central point is $(0,0,0)$. How to find out the new coordinates ...
0
votes
1answer
21 views

The Name of a Polyhedron with 6 Quadrilateral Faces, 8 Vertices, and 12 Edges

(Don't say 'cube' or 'rectangular prism') I'm looking for a generic name for polyhedra with 6 Faces, 8 Vertices, and 12 Edges where each face could be any quadrilateral shape: rectangle, rhombus, ...
2
votes
1answer
24 views

Continous family of $n$-gons

The statement of this problem asks to show that if $A$ and $B$ are two distinct convex $n$-gons there is a continous family of convex $n$-gons such that the first in that family is $A$ and the last is ...
2
votes
1answer
26 views

Two new conics associated with two triangles inscribed a conic

1-Let $ABC$ and $A'B'C'$ be two triangle inscribed a conic. Let $P$ be a point on the conic. $PA$ meets $B'C'$ at $A_1$, define $B_1, C_1$ cyclically. $PA'$ meets $BC$ at $A'_1$ define $B'_1, C'_1$ ...
2
votes
0answers
21 views

Bound on “width” of points in a plane

Suppose we define width $w(P)$ of point set $P$ in a plane to be the ratio of the maximum distance to the minimum distance between the points in $P$. (Assume unique coordinates so that $w(p)$ is ...
0
votes
0answers
19 views

How to prove that a convex polygon is cyclic

Is there an easy way to tell if a convex polygon is cyclic? I was told that if the vertices of the $n$-gon are $A_1,A_2,\ldots,A_n$, it is enough to prove that $A_1A_2A_3A_i$ is cyclic for each ...
0
votes
0answers
18 views

Using oblique projection can you always rotate a triangle to look like an equilateral triangle? [duplicate]

Starting with any triangle using oblique projection, can you view any shape triangle from an angle to see it as an equilateral triangle?
2
votes
2answers
28 views

Regular/Right hyperbolas through three points

Find all equations of regular hyperbolas passing through the points $A(\alpha,0),B(\beta,0),$ and $C(0,\gamma)$. Attempt: I am assuming here that regular means right. We can then write the ...
0
votes
1answer
11 views

Having trouble drawing an arc using atan2 and specified range of arc.

I'm writing code. My arc invariant is: $$ \theta_0, \theta_1 \in [-2\pi, 2\pi], \\ \theta_1 - \theta_0 \leq 2\pi $$ where $\theta_0$ is the arc beginning angle and $\theta_1$ is the arc end angle. ...
0
votes
1answer
16 views

scalene trapezoid point of diagonals intersection

We have a scalene trapezoid. We know AB and CD bases and the diagonal AC. Be P the point of intersection of the two diagonals. Is it possible to find the general expression for AP?
0
votes
0answers
16 views

How to rotate a 3D object, using only local x-, y-, and z-rotations, so that it always faces a camera at the origin

I have been struggling with a difficult problem involving 3D rotations. I first came across this problem in a computer science context, but I've attempted to generalize it a bit before posting. (I ...
5
votes
1answer
49 views

$\pi$ is dependent on properties of geometry, assuming that we define it as $C/d$. Could then the $\pi$ also be an integer?

$\pi$ is dependent on properties of geometry, assuming that we define it as $C/d$. Could there be a geometry where $\pi$ is a rational number or an integer?