# Tagged Questions

geometry assuming the parallel postulate of Euclid: in a plane, given a line and a point not on that line, there is exactly one line parallel to the given line through the given point.

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### Does the collection of algebraic/number-theoretic methods applied to Euclidean Geometry have a name?

I am currently writing an essay on the history of geometry. To educate myself on the subject, I sometimes read the following Wikipedia article on the history of Euclidean Geometry. It seems to me that,...
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### What is the size of the angle $\angle AMC$? [duplicate]

Suppose we have a triangle $\triangle ABC$ where the size of two angles are given: $\angle B=15^\circ$ and $\angle C=30^\circ$. We draw the median $AM$, so now what is the size of angle $\angle AMC$? ...
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### Is a shape 'polarizable'?

Given a point $p$ inside a shape $S$ described as an $n$-vertex polygon, let us say that $S$ is polar with respect to $p$ if S can be described by a polar equation $r(\theta)$ with $p$ as the origin. ...
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### Can circumscribing a circle around a polygon prove that the sum of the interior angles of an n-sided polygon is $180(n - 2)$?

I am trying to create my own proof that the sum of the interior angles in a regular polygon is $180(n - 2)$, where $n$ is the number of sides in the polygon. I have seen these proofs for this formula, ...
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### Victoria Jones want to construct a time capsule. The capsule will be right circular cylinder

Victoria Jones want to construct a time capsule. The capsule will be right circular cylinder of height 'h' cm, and radius 'r' cm on each end . Let the total volume of capsule be V cm^3. Express V in ...
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### How do curves consist of points?

According to Euclid, a point is something which has no dimensions. And we know that all curves of any type consists of points. Now this thing bothers me because if a point has no dimensions, i.e. in ...
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### New very simple Golden Number Ratio PHI construction with Circle and Two Equal Segments of Circle Diameter. Is there prior art? Proofs?

Geogebra gives me the golden number PHI to fifteen decimal places for this simple construction illustrated below wherein the ratio of the blue line i to the red line h is PHI or 1.6180.... The golden ...
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### I am going to work in SE(3) group, is vector sum approach applicable in this group?

I am working on control of mobile robot in 3d. I want to do vector sum for X and Y components, use this vector sum in control methodology and again convert resulting speeds and torques into their X ...
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### Equation for a circle in homogeneous coordinates

The equation for a circle in homogeneous coordinates is given by $(x - aw)^2 + (y - bw)^2 = r^2w^2$. I understand that the center of the circle, given by (a, b) in euclidian space is given by (a, b, ...
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### New very simple golden ratio construction incorporating a triangle, square, and pentagon all with sides of equal length. Is there any prior art?

Consider three regular polygons with 3, 4, and 5 sides wherein all the polygons have sides of equal length X throughout, as illustrated below. The ratio of the red line segment a to the blue line ...
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### Geometric Significance that 2D Points Form a Line

I'm reading through Multiple View Geometry in Computer Vision, by Hartley and Zisserman, and on page 2 it is stated that points at infinity in the two-dimensional projective space form a line, and in ...
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### New, extremely simple golden ratio construction with two identical circles and line. Is there any prior art? [duplicate]

This question is different from a previously asked question (linked above) as this golden ratio construction only utilizes two circles and a line, and is thus far simpler than the golden ratio ...
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### How to find the Coordinate equation of a curve which bends all the parallel rays from infinity towards a single point

How should I proceed on to find the coordinate equation of a curve such that it bends all the parallel rays coming from infinity towards a single point. Yes I know that it would be a 2nd degree ...
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### New Golden Ratio Construction with Two Adjacent Squares and Circle. Have you seen anything similar?

The below Golden Ratio Construction results in a ratio of PHI (1.6180...) between the blue line and red line, as found in Geogebra. This seems like a simple construction of the golden ratio, yet so ...
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### Have you seen this golden ratio construction before? Three squares (or just two) and circle. Geogebra gives PHI or 1.6180.. exactly

Note this golden ratio construction has been dramatically updated here with numerous golden harmonies: A Golden Ratio Symphony! Why so many golden ratios in a relatively simple golden ratio ...
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### Geometry Question Help

The bases of trapezoid $ABCD$ are $\overline{AB}$ and $\overline{CD}$. We are given that $CD = 8$, $AD = BC = 7$, and $BD = 9$. Find the area of the trapezoid.
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### Scalar product is 0 in any triangle

How can we prove that the following scalar product relation holds in any triangle? \left [-\overrightarrow{AB}\tan B (\tan A +2\tan C)+\overrightarrow{AC}\tan C (\tan A+2\tan B)\right ]\cdot \left (...
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### There is a square that vertices are (0,0) (0,2) (2,0) (2,2) [duplicate]

A point P satisfies following condition : The straight line passing through P and dividing the area of the square by 1:3 does not exist. Can we know the locus of P and the area of the locus ? I ...
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### How many mutually orthogonal circles are possible?

How many mutually orthogonal circles is it possible to have? It is easy to construct $3$ mutually orthogonal circles, e.g. $3$ circles with radius $1$ and centers at the vertices of an equilateral ...
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### Problems on measure of angles and arcs in a circle diagram

A friend of mine recommended this site. I cannot figure out any of the parts in the problem in the picture click here The line segments AE and DE are not tangent to the circle, so I don't know where ...
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### Does 3D euclidean space allows vector sum in 2 dimensions?

Is this right to add two orthogonal vectors to to get one vector, using this vector in calculations and after getting results, decomposing result vector to get orthogonal components? I am a programmer,...
If $A(z_1)$, $B(z_2)$, $C(z_3)$ are vertices of a triangle $ABC$ in Argand plane, what is the area of the triangle?
### There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$. A point $P$ satisfies following condition: The straight line passing through $P$ and dividing the area of square $Q$ in the ...