# 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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### Why is the max. number of intersections of k lines in $\mathbb{R}^2$ = $\binom{k}{2}$?

Why is the maximum number of intersections of k lines in $\mathbb{R}^2$ = $\binom{k}{2}$?
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### Maximize area of a rectangle between parabola and a line

I was given a task to maximize the area of a rectangle that can be inscribed between parabola $y=1-x^2$ and a line $y=0$ such that one side of the rectangle lies on the $x$ axis. My idea is to somehow ...
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### A Modern Alternative to Euclidean Geometry

First of all, I want to master Geometry, I have knowledge on high school geometry and I was thinking of learning Euclidean Geometry. I bought a copy of Euclid's Elements, it is very interesting, ...
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### Finding Height and Base of a Triangle

This is a question I got off of one of my previous math tests, and I don't even know where to start with solving it. The height of a triangle is 4 times its base. If the area of the triangle is 160 ...
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### Order Types, Point-line duality

I am trying to understand Order Types and their enumeration. I'm having a real hard time understanding these slides.. Especially the one I am showing. Could anyone explain to me what this slide from ...
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### Bounding box of a thick line with end caps

I have been pulling my hair out on the trigonometry on this and just can't seem to get it right. Basically, I need to calculate the bounding box of a line going from point (x1,y1) to (x2,y2) where ...
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### weighted integral in convex hull

Working on an integral $$J=\frac1{2\pi} \int_0^{2\pi} w(t) g(e^{it}) dt$$ where $\frac1{2\pi} \int_0^{2\pi} w(t) dt=1$ ; $w(t)$ is non-negative continuous ...
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### Point of division of line segments one is 3/4 as the other

The segment joining A(2,-4) and B(9,3) is divided into segments one which is three fourths as long as the other. Find the point of division nearer to B(9,3). I'll call the point of division as C(x,y)....
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### The locus of centre of circle tangent to two given circles

What is the locus of the centre of circles that are tangent to two given circles? I had no idea how to approach the problem so I considered a special case, namely one in which the two circles were ...
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### Why are these lines tangent?

I was trying the problems at http://euclidthegame.org and for level 20, ending up using, but couldn't see the reason behind the following: We have a circle centred on B and a point A outside the ...
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### A function similar to a rotated-sin

I would like to find a mathematical function like the one I sketched below. My first idea was to rotate a sin function, but now I don't think that would work because I would like the function to be ...
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### Can anyone calculate the area of the top shape in this diagram?

http://postimg.org/image/w5f5moq7z/ The top shape on the diagram is the sensor that I need to calculate the area for. I have tried using the 2 elipses at the side and combining them together to get a ...
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### calculate the area of this shape

It's a rectangle with 2 half elipses joined on the left and right side. The rectangle itself is 3.55 X 2.54 The width of the whole shape (rectangle with 2 elipses) is 4.195. Take away the width of ...
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### total possible triangles with integral values

How many triangles with altitudes 6,8,X(unknown value) can be formed such that the value of x is an integer?
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### Undergrad Geometry Book

What is a good follow-up to Stillwell's Four Pillars of Geometry? Also Algebraic Geometry/ Topology sounds fun -- are there any good undergrad books on that?
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### What does the rotation group of $\mathbb{\bar{Q}}^n$ look like?

There's a structural difference between the rotation groups of $\mathbb{Q}^n$ and $\mathbb{R}^n$; in some abstract sense the former is 'small' (discrete?) while the latter is 'large'. I suspect that ...
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### Vertices that create a convex quadrilateral

In how many ways can we choose 4 vertices of a convex n-gon that create a convex quadrilateral (All the inside angles are less than 180) with at least 2 sides of the quadrilateral being sides of the n-...
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### relationship between complex numbers

Consider the following: Two equilateral triangles inscribed in a circle. The vertices of the large triangle are the geometric images of the three cubic roots of $z$ (a complex number). The small ...
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### Regions of intersected hyperplanes

Let $\mathcal{A}$ be a linear arrangement of hyperplanes in $\mathbb{R}^n$ and $\mathcal{B} := \bigcap_{h \in \mathcal{A}} h$. Show that $\mathcal{C} := \{ h / \mathcal{B} : h \in \mathcal{A}\}$ ...
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### Find the circle touching a line

I have been struggling with this (probably easy to solve) geometry problem for a while. What are the coordinates of the centre and the radius of the circle?