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Systems (or computational) biologist.


Nov
18
comment Finding an angle between side and a segment from specified point inside an equilateral triangle
It's simple: note that arc length = angle (in radians) when the radius of the circle is 1 (i.e. unit circle). So when the arc length is $u$, the chord length is $2\sin(u/2)$.
Nov
15
comment Find the line that intercepts the lines $r$ and $s$ and forms congruent angles to the coordinate axes
You're almost done. From the first part of your argument, if you set $\overrightarrow{AB}=(x,\,y,\,z)$, you get $|x|=|y|=|z|$. (The angle is not 45 degrees by the way, but the argument still stands.) Then you have four cases to consider: $x=y=z$, $x=-y=z$, $x=y=-z$, $x=-y=-z$.
Nov
15
answered Nice geometry with areas
Nov
15
comment Finding an angle between side and a segment from specified point inside an equilateral triangle
I used $\cos 3\theta=4\cos^3\theta-3\cos\theta$ and $\sin 2\theta=2\sin\theta\cos\theta$. So $\cos 3\theta=\sin 2\theta$ becomes $\cos\theta(4\cos^2\theta-3)=\cos\theta(2\sin\theta)$, and dividing by $\cos\theta$ (which is not zero) we get $4(1-\sin^2\theta)-3=2\sin\theta$.
Nov
14
comment Finding an angle between side and a segment from specified point inside an equilateral triangle
A proof of $d_3+d_5=d_9$: it suffices to show $\sin 54^{\circ}-\sin 18^{\circ}=\sin 30^{\circ}$, that is $2\cos 36^{\circ}\sin 18^{\circ}=1/2$. Using the fact that $\alpha=\sin 18^{\circ}$ satisfies $4(1-\alpha^2)-3=2\alpha$ (from $\cos 54^{\circ}=\sin 36^{\circ}$), we can show that $2(1-2\alpha^2)\alpha=1/2$.
Nov
14
comment Finding an angle between side and a segment from specified point inside an equilateral triangle
This lemma is stated in www-math.mit.edu/~poonen/papers/ngon.pdf (pages 4-5). I'll check if it is really true.
Nov
14
revised Finding an angle between side and a segment from specified point inside an equilateral triangle
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Nov
14
answered Finding an angle between side and a segment from specified point inside an equilateral triangle
Nov
13
answered CD is height of right-angled triangle ABC, M and N are midpoints of CD and BD: prove AM⊥CN
Nov
13
revised How find this maximum of this $(1-x)(1-y)(10-8x)(10-8y)$
added 269 characters in body
Nov
12
comment Monoticity of power means.
Apply Hölder’s inequality. A similar argument can be found in Theorem 0.2 of ocw.mit.edu/courses/mathematics/…
Nov
11
awarded  Promoter
Nov
11
revised Translational invariance and zero eigenvalue
added 35 characters in body; edited tags
Nov
11
revised How find this maximum of this $(1-x)(1-y)(10-8x)(10-8y)$
deleted 171 characters in body
Nov
11
revised How find this maximum of this $(1-x)(1-y)(10-8x)(10-8y)$
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Nov
11
revised How find this maximum of this $(1-x)(1-y)(10-8x)(10-8y)$
deleted 1 character in body
Nov
11
answered How find this maximum of this $(1-x)(1-y)(10-8x)(10-8y)$
Nov
9
asked Translational invariance and zero eigenvalue
Sep
24
awarded  Autobiographer
Sep
1
awarded  Yearling