# 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.

2answers
69 views

### On congruent chords

Let $C_i=C(A_i,r_i)$ two secant circles intersecting each other at $R,S$, with $r_1\neq r_2$. Let $M$ be the median point of $A_1A_2$. Let $t\perp RM$ at $R$, intersecting the circles at $X,Y$. I'd ...
1answer
90 views

### Stuck at Extended Euclidean Algorithm to solve equation

I'm trying to solve the following function via the Extended Euclidean Algorithm, but I'm stuck at the last step where I need to sub in sub 2. ...
0answers
91 views

### A convex $n$-gon and the $n$-gon made by its $n$ medians

For a convex $n$-gon $P_1P_2\cdots P_n$, let $M_i$ be the mid-point of the line segment $P_iP_{i+1}\ (i=1,2,\cdots,n)$ where $P_{n+1}=P_1$. Also, let $Q_1Q_2\cdots Q_n$ be an inner $n$-gon made by $n$ ...
1answer
87 views

### Given three points, can one construct a hyperbolic curve using classical geometric construction method?

Using straight edge and compass method, can a hyperbolic curve be drawn through three given points?
2answers
365 views

### Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
3answers
217 views

### Product of rotation and translation is a rotation

I have a homework question that I'm not sure how to answer. ...
1answer
176 views

### Connecting Coordinate Geometry and Plane Geometry

What is it that allows us to take theorems proven in Euclidean geometry (i.e. with Euclid's five postulates or Hilbert's Axioms) and then apply them outside of Euclidean geometry. For example in ...
2answers
48 views

### How does this proof of law of sines determine equal angles?

I was reading over this proof of the law of sines and they say that $\angle CAB = \angle DOB$ because of "basic geometry". I do not get it though, how can you say that the angles are equal?
2answers
382 views