Tagged Questions

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
votes
1answer
24 views

Equation of a specific shape's edge?

Suppose we have such a shape: It is needed to found what this shape's edges are. I mean, this shape edges are: outer arc (upper) - we know everything we would like about this arc: radius, start ...
0
votes
3answers
19 views

Cyclic quadrilaterals - finding the size of an angle

I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question ...
0
votes
0answers
14 views

Cover points with specified amount of cuboids and minimize overlap

Given a list of Points (the coords are pure integeres), I want to cover all of them with cuboids. The Problem is, I have a limited number of cuboids I can use. Of course I would like to have a ...
1
vote
1answer
20 views

Area of a triangle.

The area of a triangle $ABC$ is $144$.Denote the midpoint of $BC$ by $P$,of $AP$ by $Q$ and of $AC$ by $R$.Calculate the area of the triangle $PQR$. I draw the picture but I do not have any idea to ...
2
votes
0answers
24 views

Calculate the distance between any points in two different circles

I have two overlapping circles (C1 and C2) for which the distance between their centers is know. Inside each circle theres's random number of points (P11... P1n and P21... P2n) for which the distance ...
0
votes
1answer
25 views

Estimating the missing points of a 3D point cloud

Consider a cloud of N points (forming a smooth 3D object), in which n points are missing. Also, consider that there is no prior knowledge about the original shape of the point cloud. The only ...
-2
votes
1answer
17 views

Bi-conditional statement

Can a bi-conditional be written with these 2 statements? If 3 points are collinear then they are coplanar. If 3 points are coplanar then they are collinear.
2
votes
1answer
49 views

Moving a point around a circle

we're currently working on a game which involves a character that rotates around a point. We are using a rotation matrix to rotate a given a point (x,y) around another point by first translating to ...
4
votes
1answer
36 views

Dividing a disc into equal parts

Prove that it is not possible to divide a disc into $7$ parts of equal area by means of three straight lines. Background: I saw this question asked in a way which seemed to imply the possibility ...
1
vote
1answer
17 views

If two harmonic quartets have a common point, prove their lines are concurrent

Let $A,B,C,D$ and $A,L,M,N$ be collinear points such that $\{AB,CD\} = \{AL,MN\} = -1$. Prove that the lines BL, CN and DM concur. I tried to build a triangle using A as a common point and then use ...
1
vote
1answer
30 views

How to work out side length of a square with 3 unit circles

How do you work out the side length of a square which contains 3 packed circles of radius 1: "Circles packed in square 3" by Toby Hudson - Own work. Licensed under Creative Commons ...
1
vote
0answers
18 views

Find all regions formed by a set of circles

I was doodling with Python to draw some circles, and I was able to find all intersection points of a set of random circles, yay ! Now I'm stuck on a question, is there a way to find all regions ...
1
vote
2answers
63 views

the set of points equidistant from $ u $ and $v$ form a line.

Let $u$ and $v$ be two vectors in $ \mathbb{R}^2 $ with the standard norm. Show that the set of points equidistant from $ u $ and $v$ form a line. I show that if $x$ is equidistant from $u$ and $v$, ...
0
votes
0answers
23 views

Determine sine wave frequency from two arbitrary points

If I have only two arbitrary points on a sine wave, what would be the simplest method for determining the frequency of the sine wave? The frequency is unknown. The bandwidth is restricted, the time ...
1
vote
3answers
15 views

Find the radii of the two circles which pass through the point $(16,2)$ and touch both axes

How can I find the radii of the two circles which pass through the point $(16,2)$ and touch both the axes? I've only ever seen demonstrations using three normal co-ordinates; or two normal ...
-1
votes
1answer
23 views

Find Equation of Parabola

I am trying to get my head around parabolas and running into bit of a wall. I've been trying to figure out what the formula for a parabola would be given that i have 2 points on Cartesian plane ...
0
votes
1answer
15 views

Prove that Lorenz's Postulate is logically equivalent to Parallel Postulate 5

Lorenz, Every single line through a point within an angle will meet at least one side of the angle. I know I have to Show that the parallel postulate 5 implies lorenz, and then lorenz implies ...
4
votes
1answer
31 views

Find the missing angle of similar triangle

Find the missing angle $\theta$ in the triangle below given that $R>r$, $l\geq R$, $0< \theta < \frac{\pi}{2}$. Attempted Solution I attempted to use similar triangles to find the angle ...
1
vote
2answers
30 views

Algebra Logical Pythagorean theorem help

A wire is attached to the top of a pole. The pole is 2 feet shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 feet less than the length of the wire. ...
1
vote
2answers
28 views

How to check if a 3D line segment intersects a cylinder?

I have developed a check for a 2D case of a circle intersecting a 2D line segment, however there is a particular case that I can't figure out how to extend to 3D: If one endpoint on the 3D line ...
1
vote
1answer
26 views

Finding the intersection points of two circles algebraically

I need to find the intersection points of two circles with equations: $(x+1)^2+(y-1)^2=1$ and $(x-1)^2+(y+1)^2=4$. I understand how to find the points by plotting the circles but I am unsure of how ...
11
votes
1answer
115 views

Largest $n$-vertex polyhedron that fits into a unit sphere

In two dimensions, it is not hard to see that the $n$-vertex polygon of maximum area that fits into a unit circle is the regular $n$-gon whose vertices lie on the circle: For any other vertex ...
0
votes
0answers
13 views

Applying homography to ellipse derived from normal distribution

I need to apply a homography to an elliptic area. First question: Is the resulting also elliptic in every case? I think so, but actually i don't really know. Anyway, I assume it for this question. ...
2
votes
0answers
18 views

Right angle triangle with integral vertices [duplicate]

There is right angled triangle with known lengths for each side. Is there a known method to check if all the vertices will be integers if that triangle is placed anywhere on the plane? (or) what is ...
2
votes
2answers
134 views

Need some help solving high-school level trignometry question.

here it is. I've tried solving it multiple ways but it gets too complicated. Is there any way to solve this?
0
votes
1answer
19 views

Observation about SSA criteria.

IS the following observation true in general? I nned some help please.
0
votes
1answer
11 views

Analyze growth using graphs

How do I analyze growth using only graphs (and no exact values)? I want to show that the first growth is cubic, the second is square and the third is linear. As far as I know the third one can be ...
4
votes
2answers
64 views

Is HHH a congurence criteria for triangles?

I wanted to know if a triangle defined by its 3 heights is unique. I took this up as a challenge but was able to get nowhere, can anyone help me? :)
2
votes
1answer
30 views

When is $3R\le 2h_{\max}$ true for acute triangles?

I was working on a problem recently, and it happened that it could be solved if $3R\le 2h_{\max}$ was true for all acute angled triangles. So I used GeoGebra to check it, and found that for some ...
3
votes
3answers
147 views

Drawing a Right Triangle With Legs Not Parallel to x/y Axes?

I have been presented with an interesting problem. How can I decide whether a right triangle with given side lengths can be placed (with integer coordinate vertices) on a Cartesian plane so that the ...
0
votes
2answers
24 views

Proove the following using either Direct Proof, Contrapostive and Contradiction. (Question related to Geometry).

A circle has centre $(2,4)$. Prove that if $(0,3)$ is not inside the circle, then $(3,1)$ is not inside the circle. I just want to know if my method would be correct. The method I used is as follows: ...
2
votes
1answer
31 views

The reflection of $f(x,y) = x^2 - y^2$

How would I make a reflection of $$ f(x,y) = x^2 - y^2 $$ along the z axis? Beacuse if if write $$ f(x,y) = -(x^2 - y^2) $$, flips the figure along the XY axis...
0
votes
1answer
17 views

How many milliliters of liquid to fill [duplicate]

A right circular cone has a depth of 103 mm and a top diameter of 82.4 mm. The cone contains water to a depth of 30.0 mm. How many more millilitres of liquid need to be added in order to fill the ...
2
votes
0answers
55 views

area estimation with tiling

For any given shape drawn on a graph paper, a kid can calculate the area of any shape by counting the tiles with a simple formula: any edge covering 50% or more, mark the tile; total area = sum all ...
0
votes
1answer
20 views

How to sort vertices of a polygon in counter clockwise order?

How to sort vertices of a polygon in counter clockwise order? I want to create a function (algorithm) which compares two vectors $\vec v$ and $\vec u$ which are vertices in a polygon. It should ...
0
votes
2answers
34 views

Parametric form of square

What is the appropriate parametric equation of the boundary of a square? For example, the unit circle has a parametric equation $x(t)=\cos(t)$ and $y(t)=\sin(t)$.
2
votes
1answer
42 views

Area of octagon constructed in a square

The following picture is constructed by connecting each corner of a square with the midpoint of a side from the square that is not adjacent to the corner. These lines create the following red octagon: ...
5
votes
1answer
53 views

What is the equation of the reflections of a fixed point across all the tangents to a fixed circle?

Given a fixed circle "c" and a fixed point "A" (in the plane of the circle), draw the tangent to the circle at a variable point "X" (movable, but constrained to be on the circle), reflect "A" across ...
4
votes
1answer
29 views

What is the maximal size of an equal-distance set in $\mathbb{R}^n$?

Let $A\subseteq \mathbb{R}^n$ with the casual metric and $c\in\mathbb{R}^+$ be a real positive number, such that for every $a_1, a_2\in A$ if $a_1\neq a_2$ then $d(a_1,a_2)=c$. What is the maximal ...
1
vote
0answers
26 views

Find the length of the longer diagonal on a trapezium with only 2 sides stated.

Im at a loss here, i know i have to divide the trapezium, but im still not sure which calculation is relevant to it then. Thanks in advance.
0
votes
0answers
46 views

How to solve Alhazen's problem with marked ruler and compass?

According to Robin Hartshorne (in Geometry: Euclid and Beyond, pg. 278), Alhazen's problem is solvable with marked ruler and compass (because it's equivalent to solving a quartic equation). I would ...
3
votes
2answers
52 views

How calculate the shaded area in this picture?

Let the centers of four circles with the radius $R=a$ be on 4 vertexs a square with edge size $a$. How calculate the shaded area in this picture?
3
votes
1answer
52 views

Areas between intersecting chords

In the circle below let the two chords be called $C_1$ and $C_2$, and their intersection be some point that is not the center. The chord power theorem tell us that $a \cdot b = c \cdot d$. I am ...
1
vote
1answer
16 views

Right triangle inscribed in a circle with the equation of the circle is $r=2a\:cos\left(\theta \right)$

How to prove that the equation of the circle (the image given below) is $r=2a\:cos\left(\theta \right)$ using polar coordinates? Please anyone help me, I've been stuck in this problem for like 2 hours ...
1
vote
2answers
59 views

How is it called when one ellipse is “more elliptical” than another one?

Assume you have two ellipses, $A$ and $B$. Now $A$ looks "flatter" than $B$ because its ratio $\frac{\text{major axis}}{\text{minor axis}}$ is bigger. This means it "looks less" than a circle. How is ...
0
votes
0answers
20 views

reparametrized geodesics

I am doing this exercise : Let $X$ be a metric space. A continuous path $c : I → X$ is a linearly reparameterized geodesic if and only if $d(c(s), c(t)) = 2 d(c(s), c((s + t)/2))$ for all $s, t ∈ I$; ...
0
votes
2answers
46 views

Math homework, so much guessing work? [closed]

Riki hires a digger to load topsoil onto his trailer. The bottom of the trailer is square with sides 1.5 meters long. The height of the sides of the trailer is 25 centimeters. The digger shovel holds ...
12
votes
1answer
125 views

Koch snowflake versus $\pi=4$

The only proof I could find of the Koch snowflake having infinite perimeter was by calculating the perimeter $P_n$ after the $n$th iteration $$P_n = 3s\left(\frac{4}{3}\right)^n,$$ where $s$ is the ...
2
votes
1answer
18 views

Finding the polar line of the intersection of a polar line and a tangent

Let $K$ be an inversion circle with center $O$ and let $C$ be the point of intersection of two lines tangent to $K$ in $A$ and $B$. Then let $E$ be the intersection of the line $AB$ and the line ...
0
votes
2answers
34 views

How many milliliters to fill cone

A right circular cone has a depth of 103 mm and a top diameter of 82.4 mm. The cone contains water to a depth of 30.0 mm. How many more milliliters of liquid need to be added in order to fill the ...