3
votes
1answer
168 views

Finding the shortest path length on a curved surface(hyperboloid)

I wish to find the minimum path length between two points $P_1(\sqrt2,0,-1)$ and $P_2(0,\sqrt2,1)$ on a hyperbolic surface $S =\{(x,y,z)\in R^3\ |\ x^2+y^2-z^2=1\}$ I faintly recall studying ...
1
vote
0answers
58 views

How surfaces intersect in projective spaces

Consider this parametrization $$\phi:\mathbb{P}^1\longrightarrow\mathbb{P}^3$$ $$(t_0:t_1)\longmapsto (t_0^3: t_0^2t_1:t_0t_1^2:t_1^3)$$ Let $\mathcal{C}$ be the image of $\phi$. I've proved that ...
3
votes
6answers
2k views

Maths GCSE very hard question

My friends recently took a Maths GCSE. In the paper, they came across a very difficult question which we spent a full half-hour train journey trying to figure out. We didn't manage it, so I've come ...
2
votes
2answers
158 views

Solving for the length of a side of a triangle

I have a problem in which I'm supposed to solve for the length of the two sides of the triangle below. I assumed that it would simply boil down to $x+5=\sqrt{4x+52}$, and converted to standard form, ...
3
votes
2answers
276 views

How do you find the vertex of a (Bézier) quadratic curve?

Before I elaborate, I do not mean a quadratic function! I mean a quadratic curve as seen here. With these curves, you are given 3 points: the starting point, the control point, and the ending point. I ...
3
votes
1answer
253 views

Recursive sequence and a quadratic equation related inequality proof

I am trying to show that if a sequence of number $x_{n}$ is defined by $x_1 = h$, $x_{n+1}=x_n^2 + k$, where $0<k<\frac{1}{4}$ and $h$ lies between the roots $a$ and $b$ of the equation $$x^2 -x ...
3
votes
1answer
160 views

Close Packing of Ellipsoids

How can the packing density of a set of congruent ellipsoids be calculated? I'm dealing with prolate spheroids so technically I do not need the general answer for ellipsoids, but my abstract mind ...
5
votes
2answers
591 views

Find equation of quadratic when given tangents?

I know the equations of 4 lines which are tangents to a quadratic: $y=2x-10$ $y=x-4$ $y=-x-4$ $y=-2x-10$ If I know that all of these equations are tangents, how do I find the equation of the ...