The mathematician formerly known as DayLateDon

1d
revised What is the isotomic conjugate version of the six point circle of isogonal conjugates?
added 329 characters in body
1d
awarded triangle
1d
awarded Revival
1d
awarded Enlightened
1d
awarded Nice Answer
1d
awarded Good Answer
2d
comment How to find the focus of a parabola
This answer to a related question indicates how to find the focus. Remaining elements are pretty straightforward.
2d
comment Why does this proof by bashing not work?
"If I did the algebra right wouldn't it need [to] return $-1$?" Yes. So, the conclusion is that you didn't do the algebra right. Although most of it looks correct (congratulations!), I get a different $y$-coordinate for $O$.
Apr
16
revised An ancient Japanese geometry problem.
added 19 characters in body
Apr
16
revised An ancient Japanese geometry problem.
deleted 67 characters in body
Apr
16
answered An ancient Japanese geometry problem.
Apr
15
comment An ancient Japanese geometry problem.
This PDF of the book seems to have this as Problem 3 of Chapter 6 (pg 194), except that the book includes one important addition: $\overline{CH}\perp\overline{AP}$ (in the notation of the problem as given above).
Apr
15
answered sum of the squares of the reciprocals of the two parts of the focal chord of a parabola
Apr
15
comment An ancient Japanese geometry problem.
@LuisGomezSanchez: You should describe your solution, so that we don't duplicate your effort.
Apr
14
comment Hyperbola - the average of the angle between the tangent and the line to the focal point
@SamZaid: Your intuition about "infinitesimal units" doesn't seem correct. Generally, the "average value" of a function $f(x)$ for $a \leq x \leq b$ is given by an integral $$\frac{1}{b-a}\;\int_a^bf(x)\;dx$$ Consider this example: $f(x) = x^{-2}$, as $x$ varies from $1$ to some $N$. The average value is $$\frac{1}{N-1}\;\int_1^{N} x^{-2}\;dx = \frac{-1}{N-1} x^{-1}\left.\right|_1^N = \frac{-1}{N-1}\left(\frac{1}{N}-\frac{1}{1}\right) = \frac{1}{N}$$ As $N$ approaches infinity, the average value approaches the limit of zero. This, even though $f(x)$ itself is strictly positive.
Apr
14
comment Hyperbola - the average of the angle between the tangent and the line to the focal point
For points way out on the hyperbola, the tangent line and the line to the focus are very-nearly parallel, so that the angle between them is effectively zero. Because the hyperbola extends infinitely, any "average angle" computation will be overwhelmed by these vanishingly-small values; the average will be zero.
Apr
12
comment Derivatives of hyperbolic functions and Osborne's rule.
For the curious, Osborne's Rule is described here, and it shows how to translate an identity from (circular) trigonometry into its counterpart in hyperbolic trigonometry. Now, since derivative formulas are not trig identities, there's no reason to expect Osborne's Rule to apply.
Apr
12
revised Names-to-Numbers puzzle
Re-formatted
Apr
12
revised Prove a trigonometric identity
TeXification, better title
Apr
10
answered What comes after seconds?
1 2 3 4 5