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
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2answers
25 views

calculate arbitrary points from a plane equation

I understand how one can calculate a plane equation (ax+by+cz=d) from three points but how can you go in reverse? How can you calculate arbitrary points from a plane equation?
0
votes
1answer
14 views

Find the triangle with the greatest area using trigonometric ratios

The hypotenuse, c, of right $\triangle$ABC is $7.0$cm long. A trigonometric ratio for angle $A$ is given for four different triangles. Which of these triangles has the greatest area? a) sec $A$ = ...
-1
votes
0answers
27 views

A geometric inequality about the internal besectors [closed]

prove that in every triangle the following inequality is hold: $$\frac{1}{w_\alpha}+\frac{1}{w_\beta}+\frac{1}{w_\gamma}\le \frac{2}{\sqrt{3}}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$$ ...
2
votes
1answer
84 views

Volume from equation $(x ^2+ y ^2 + z ^2 ) ^2 = xyz$

How can you calculate the volume of the shape represented by the following equation: $$(x ^2+ y ^2 + z ^2 ) ^2 = xyz$$ I tried converting it to polar form (so $r = ...
0
votes
0answers
24 views

area and fixed perimeter

I need help. Can someone please explain and demonstrate in a very easy way why: With a fixed perimeter the equilateral triangle has a bigger area With a fixed perimeter square has a bigger area ...
1
vote
3answers
42 views

Common perpendicular of two straight lines

I have the straight lines: $$d_1: \frac{x-1}2=\frac{y-3}1=\frac{z+2}1\\[4ex] d_2: \dfrac{x-1}1=\frac{y+2}{-4}=\frac{z-9}2$$ And I have to find the common perpendicular of these lines.
0
votes
2answers
32 views

How do I find the angle between 2 forces?

If have a resultant force $F_R = (3i + j - k)$ and and component of that force is $F_1 = (2i - 2j + k)$. How do I find the angle between these 2 forces?
-1
votes
2answers
41 views

How would the volume of a frustum with irregular polygon area be calculated?

I want to calculate the volume of this shape, it's basically a frustum with an irregular polygon base. The bottom area $A_1$, the height of the frustum shape $h$,the sideways distance between $A_1$ ...
0
votes
1answer
20 views

perimeter finding on triangle LMO

Triangle LMO has vertices with the following coordinate points: L (4, 4) M (0, 0) O (4, 0) how can I find its perimeter? I don't know how to find the hypotenuse please help
1
vote
1answer
42 views

Locus of centers of circles through a given point and tangent to a given line

I want to find the locus of points of the centers of circles that pass through some point, say $(x_0,y_0)$, and are tangent to some line, say $Ax + By - C = 0$. I guess the locus is going to be ...
0
votes
1answer
7 views

Given points $A$ and $B$, what curve does the locus of points that form congruent angles take?

In more mathematical terms, let $X$ be the set of points that satisfy the following condition: $\forall \, C \in X, \, m \angle ACB = k$ where $k$ is some positive real value less than $180^{\circ}$. ...
2
votes
0answers
22 views

Estimating the volume of a beerglass

Most who have been to college recognizes the red glasses used for beerpong and alcohol consumption. My question is about why one method is better at estimating the volume and why. The exact volume ...
1
vote
0answers
27 views

Prove a harmonic range from a familiar picture

During solving some simple problem (10th grade), I found this interesting problem, which I got no clue to solve it clean and properly. Hope someone can give me some hint to solve it. Thanks. Given ...
0
votes
2answers
21 views

ABCD is a square. A point M is taken on side CD…

$ABCD$ is a square. A point $M$ is taken on the side $CD$; $K$ is the point of intersection of the side $BC$ and the bisector of the $\angle{BAM}.$ Prove that $MA=BK+DM $. I found this on a ...
0
votes
0answers
13 views

Convex figure is equal to intersection of supporting half planes

Prove that for any closed, convex, figure $\mathcal{F}$ in $\mathbb{R}^2$ $$\mathcal{F} = \bigcap_{H \supset \mathcal{F}} H$$ where $H$ is any supporting half plane of $\mathcal{F}$. We know that ...
-1
votes
2answers
21 views

How to find a point a plane?

Consider the noncoplanar vectors OA(1, -1, -2), OB(1, 0, -1), OC(2, 2, -1) related to the orthonormal basis (i, j, k). Let H be the foot of the perpendicular through O and the plane ABC. Determin the ...
0
votes
1answer
19 views

Finding side of a triangle, given two sides and angle bisector

Given : $\triangle ABC$, $AB=7$,$AC=9$, the angle bisector of $\angle BAC$ passes through BC in point D such that $AD = BD$, find BC. Here is drawing I have no idea who do start with this one.
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0answers
25 views

Volume question regarding segmenting a truncated cylinder.

Picture of a truncated wedge segment 2If you segmented a truncated cylinder, ensuring all segments had the same volume, where would the intersection be? I'm understand there'll probably not be a ...
0
votes
2answers
45 views

Solve a geometry problem by using vectors.

In triangle $ABC$, the bisector of angle $A$ meets side $BC$ in point $D $ and the bisector of angle $B$ meets side $AC$ in point $E$. Given that $DE$ is parallel to $AB$, show that $AE = BD$ and that ...
1
vote
1answer
45 views

What are some ways to check if a the information given is enough to solve a problem related to euclidean geometry? [closed]

To know if a the data given produces a unique answer is something important because if you know the data is insufficient to yield a unique answer you can stop looking for one. Example: $\triangle ...
0
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0answers
31 views

Recommend guide book of algebraic geometry [duplicate]

I have a little knowledge about geometry and algebraic topology . I want to learn some basic conception and thought of algebraic geometry. Besides , I want to know main of theory of sheaves. What book ...
3
votes
2answers
96 views

Geometrical Interpretation of Tensors (intuition)

How would one describe to a non-mathematician (an undergraduate physicist actually- so please do use mathematics-i am not even sure if they can be described without mathematics!) what do tensors ...
0
votes
0answers
25 views

How do i compute how much i can rotate my tool?

I am at moment trying to implement an Ball tracker for a robot arm with a stereo camera monted on it as its tool. Illustration: http://m.imgur.com/5oojXdh The camera provide me with an dx, dy, dz ...
0
votes
1answer
36 views

Find the other 2 interior angles of pentagon inscribed in a circle given 3 angles.

Given a pentagon $ABCDE$ inscribed in a circle with centre $O$. Three of the interior angles are $95^°$, $130^°$ and $138^°$. Find angle $x$ and $y$. I'm quite sure that $x$ and $y$ can be found as ...
-2
votes
1answer
72 views

How to find the correct value of pi? [duplicate]

Pi is defined as the ratio of $\frac{c}{r}$. Many ancient scintist try to find the value of pi. Some of the values are $\frac{22}{7}$(good hold upto 10 decimal point), $\frac{355}{113}$ (good hold ...
1
vote
1answer
15 views

Construction of an $n$-Sphere

I have been thinking about various ways to construct an $n$-sphere. Starting with $S^2$, we can construct it by taking two disks, lifting the "meat" of the disks into a third dimension and then ...
3
votes
1answer
59 views

Why does $\left(\frac b2\right)^2$ "geometrically complete the square?

I was just reading this MathisFun article on completing the square. It states that geometry can help complete the square. It starts off with a square and a rectangle (pictures come from link): ...
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1answer
25 views

Intersecting three rays and a sphere of known radius

So I actually solved this problem using an iterative solver, but it annoys me because as far as I can tell it should be possible to do it directly. I have three known 3D "rays" that all start at the ...
2
votes
2answers
73 views

How to solve this geometry problem which involves triangles and triangulation

I need to solve this trig problem. Can you please help me? Based on this image: I need to calculate $PO$ based on the values of $\alpha$, $\beta$ and $AB$ ( Assume that I know the values of ...
0
votes
1answer
38 views

Computing the Manhattan Distance between two clusters of points. [closed]

We have two clusters of points: c1: (1, 1), (1, 2), (1, 3) c2: (2, 7), (2, 8), (2, 9) I know the Manhattan Distance formula is as follows: $d(a,b) = \sum|b_i - ...
0
votes
1answer
77 views

Prove that $R_1+R_2+R_3=R+r$,where $R$ is the circumradius and $r$ is the inradius of $\triangle ABC.$

Consider a triangle $DEF$,the pedal triangle of the triangle $ABC$ such that $A-F-B$ and $B-D-C$ are collinear.If $H$ is the incenter of $\triangle DEF$ and $R_1,R_2,R_3$ are the circumradii of the ...
0
votes
1answer
56 views

Prove that $2A+A_0=A_1+A_2+A_3$,where $A$ is the area of the triangle $ABC.$

If $A_0$ denotes the area of the triangle formed by joining the points of contact of the inscribed circle of the triangle $ABC$ and the sides of the triangle;$A_1,A_2,A_3$ are the corresponding areas ...
0
votes
1answer
19 views

Prove that there is at least one acute triangle from 5 segments, each 3 of them form a triangle

I found the following problem - there are 5 segments given. Each three of them can be used to form a valid triangle. I need to prove that there is at least one acute triangle among all possible ...
0
votes
1answer
19 views

Decompose any real square matrix in geometrically interpretable matrices

Is it possible to decompose any real square matrix in a product of simple linear maps such as shear, reflection, squeeze, scale and rotation? I think that would provide great insights about the ...
0
votes
1answer
26 views

What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle?

What is the length of the shorter trisector of the right angle in a $3$-$4$-$5$ triangle? I found this question in a local question paper, and I am unable to solve it. I applied Cosine formula, ...
0
votes
3answers
44 views

geometry - find a point equidistant from three other points

This problem appears in a contest. Can anyone tell me what is the quickest way to solve the problem? Time is a key factor in solving this problem. Thank you very much! Problem: Find the coordinates ...
2
votes
0answers
15 views

Number of simplices of convex hull of points on a $d$-sphere.

I was discussing this with my professor the other day and he left me to figure out. And I can't for the life of me, figure out why this is so. I would appreciate what I should look into rather than an ...
0
votes
0answers
7 views

Building a convex set out of two convex sets where each extremal point of one set shares and edge with each extremal point of the other [duplicate]

Consider a convex set $P$ with two faces $f_1, f_2$ s.t. all extreme points of the convex set belong to either $f_1$ or $f_2$ (but none blong to both - the two faces are disjoint in the set of ...
-2
votes
4answers
48 views

Geometry Problem. [closed]

ABCD is a square. Parallel lines m, n, and p pass through vertices A, B, and C, respectively. The distance between m and n is 12, and the distance between n and p is 17. Find the area of square ABCD.
0
votes
1answer
29 views

Two triangles in a plane

Let $\Delta_1$ and $\Delta_2$ be two triangles in a plane with centroids $G_1$ and $G_2$ respectively. Let $X$, $Y$ be variable points on the perimeter of the triangles $\Delta_1$,$\Delta_2$ ...
3
votes
2answers
44 views

If $r$ is the inradius of $\triangle ABC$,then prove that $\frac{2}{r}=\frac{1}{r_a}+\frac{1}{r_b}+\frac{1}{r_c}$

In acute angled triangle $ABC$,a semicircle with radius $r_a$ is constructed with its base on $BC$ and tangent to the other two sides.$r_b$ and $r_c$ are defined similarly.If $r$ is the inradius of ...
0
votes
0answers
13 views

How to derive the five-segment axiom of Tarski's geometry from Hilbert's axioms?

We are trying to prove that in an arbitrary Hilbert plane (assuming Hilbert's axioms of Group I:Incidence, II:Order and III:Congruence https://en.wikipedia.org/wiki/Hilbert%27s_axioms), Tarski's ...
2
votes
1answer
41 views

Prove that $DQ \times DB = DP \times DC + DR \times DA$.

Let $ABCD$ be a parallelogram, with $P$, $Q$, and $R$ the points on which a given circle passes through $D$ and cuts through the segments $CD$, $BD$ and $AD$ respectively: How do you prove that $DQ ...
0
votes
0answers
17 views

If point (cos(theta),sin(theta)) does not fall in the angle btw the lines y=|x-1| in which the origin lies then find the interval which theta belong

I don't get what is the condition for a point to lie between acute or obtuse angled region of two intersecting lines
1
vote
3answers
19 views

Geometry, Intersection of Spheres

Can someone explain why the intersection of the unit sphere centred at (0,0,0) an the unit sphere centred at (1,0,0) is a circle of radius $\frac{\sqrt3}{2}$ in the plane {$x_1$=1/2}, centred at ...
0
votes
1answer
12 views

Is the simplicial join of two spherical simplicial complexes itself spherical?

I think this ought to be true, but I am struggling to see why. Of course if one of the spheres is $S^0$ then this is trivially true, as we are just glueing two cones along their boundary. I'm not ...
0
votes
0answers
24 views

Area of “tubular” neighbourhood of a curve

Assume $\gamma$ is a $C^1$ curve $\gamma: [0,\epsilon]\rightarrow U\subset \mathbb{R}^2$ which is tangent to a continuous non-vanishing vector field $X=\frac{\partial}{\partial x} + ...
0
votes
2answers
89 views

Help with complex numbers geometry proof

See this link. The last step is skipped, because it is claimed to be trivial, but apparently there is a gap in my knowledge. $M$ is $\frac{1}{2}(b+c)$ and $H$ is $\frac{1}{2}i(b+c)$, but how do you ...
0
votes
0answers
15 views

How do I prove this simple result for the face structure of convex sets?

I have a convex set $P$ with faces $f_1, f_2$ such that all extremal points of the convex set belong to either $f_1$ or $f_2$ (the faces are disjoint and cover $P$). How can I prove that if every ...
0
votes
1answer
16 views

Angle of rotation based on apparent change in size

I have a camera set up which views an object in 2D in front of it square on that's 309mm away, the object changes in size by 0.073mm. What I am trying to calculate is by what angle has the object to ...