Tagged Questions
1
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2answers
87 views
Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$
There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
0
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1answer
54 views
What is “degenerate” about degenerate quadratic surfaces?
In Wikipedia the table of quadratic surfaces is divided into 2 parts, the second being "degenerate quadrics". Why is this distinction made? and what does the word degenerate means in this case?
1
vote
2answers
243 views
Is the area of intersection of convex polygons always convex?
I am interested specifically in the intersection of triangles but I think this is true of all convex polygons am I correct? Also is the largest possible inscribed triangle of a convex polygon always ...
0
votes
1answer
96 views
Spherical coordinates to cartesian coordinates.
I want to find out the distance between the centers of $2$ circles.
Say, circle $1$ $(\theta,\phi)$
circle $2$ $(\theta,\phi)$
The radius of this circle is found using $d\tan(\theta)$
where $d$ is ...
1
vote
0answers
73 views
Polynomial function from $S^3$ to $S^3$ and quaternions
I am searching the polynomial functions from $S^3$ to $S^3$.
We say $g$ is a polynomial function from $S^3$ to $S^3$, if there exists $f_1,f_2,f_3,f_4 \in \mathbb{R}[X_1,X_2,X_3,X_4]$ and
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10
votes
2answers
587 views
Software for solving geometry questions
When I used to compete in Olympiad Competitions back in high school, a decent number of the easier geometry questions were solvable by what we called a geometry bash. Basically, you'd label every ...
