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Results tagged with curves
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user 122662
0
votes
Divide angles by coefficients relate to Fibonacci sequence
Locus equation of the point $O_1$, In Cartesian coordinates, as follows:
$$x=\frac{1}{2}t\frac{t^2-3}{t^2-1}$$
$$y=\frac{1}{2}\frac{t^2+1}{1-t^2}$$
where $-1<t<1$ or the equation:
$$x^2-y^2=\frac{2y^ …
- 1,776
7
votes
1
answer
664
views
A problem of four conics
I found a remarkable theorem of four conics as follows some years ago. But it has no proof; I am looking for a proof:
Theorem: Take three conics. Suppose that each of them touch a fourth conic at two …
- 1,776
0
votes
1
answer
208
views
Divide angles by coefficients relate to Fibonacci sequence
In the left Figure, consider a right triangle $OPA$ with $\angle {AOP} = 90^\circ$. Let $\ell$ be the reflection of $PO$ in $PA$ and $\ell$ meets $OA$ at $A_1$. Let $O_1$ be the center of the circle …
- 1,776