The mathematician formerly known as DayLateDon

1d
revised How to divide trigonometric ratios using identities?
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1d
comment Why is Euclid's proof on the infinitude of primes considered a proof?
"Then P(1)+P(2)+.........+P(N)+1 is not divisible by any prime that you know." This is true. "Therefore P(1)+P(2)+.........+P(N)+1 is also a prime." This does not follow. The first statement merely implies that there must exist a prime that you don't know; the unknown prime may or may not be P(1)+P(2)+.........+P(N)+1, but that doesn't matter to the proof.
1d
comment Prove that $\angle DAP=\angle CAB$ in a parallelogram $ABCD$
@Pp..: I'm glad that made sense, even though I had mistakenly referred to point $D$ as point $C$ in my comment. :/
1d
revised Find sides and height of isosceles trapezium given information about its diagonals
More-informative title
1d
comment Prove that $\angle DAP=\angle CAB$ in a parallelogram $ABCD$
@Pp..: Constructing from the conclusion is kinda cheating, isn't it? ;) As for the circle: As Jack mentions, the products $BK\cdot BC$ and $DL\cdot DC$ calculate the power of points $B$ and $C$ with respect to some $\bigcirc CKL$. Such power is also equal to $r^2-d^2$, where $r$ is the circle's radius and $d$ a pt's distance from the center. With respect to a circle with a given $r$, since (by assumption) the powers for $B$ and $C$ match, their "$d$"s must match, too. That is, the center of $\bigcirc CKL$ is equidistant from $B$ and $C$: it's on the perpendicular bisector of $\overline{BC}$.
1d
comment Prove that $\angle DAP=\angle CAB$ in a parallelogram $ABCD$
For those looking to construct this figure: Take $O$ a point on the perpendicular bisector of $\overline{BD}$, and consider $\bigcirc O$ that passes through $C$. Then $K$ and $L$ are the other points where $\bigcirc O$ passes through the specified edges of the parallelogram.
2d
awarded Good Answer
2d
comment Can this be proven for any maze?
If the goal is in the "center" of the maze, the hand-on-the-wall strategy may not work. (Consider a box in the center of a room. Keeping a hand on a wall of the room will take you round and round and round, but you'll never get to the box.)
Jan
22
comment Show that $1+z=2\cos\frac 12\theta(\cos\frac 12 \theta + i\sin \frac 12 \theta)$
@Gummybears: $z$, $1+z$, $1$, and $0$ are vertices of a rhombus.
Jan
22
comment Archimedean Arbelos: seven circles with many properties
The Cut-the-Knot article walks through a proof using inversion; I don't know where one might find a downloadable version. I gave an inversion-less solution to a problem related to the Twin Circles here that may-or-may-not be helpful. If inversion is off-limits, then how about Descartes' Theorem for Tangent Circles? With it, you can deduce the radius of the twin circles; and, thanks to Jack's figure, you see that you only need check that the red triangle's inradius matches.
Jan
22
awarded Nice Answer
Jan
22
revised I can't remember a fallacious proof involving integrals and trigonometric identities.
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Jan
22
revised I can't remember a fallacious proof involving integrals and trigonometric identities.
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Jan
22
comment I can't remember a fallacious proof involving integrals and trigonometric identities.
You beat me by 8 seconds! I'm leaving my answer up, anyway. :)
Jan
22
answered I can't remember a fallacious proof involving integrals and trigonometric identities.
Jan
21
comment Prove that two segments are congruent in the arbelos
It turns out that Cut-the-Knot has a discussion of the twin circles, and a spare! The inversive proof there may relate to the argument hinted-at by Boas for this problem.
Jan
21
comment Archimedean Arbelos: seven circles with many properties
$\Gamma_4$ and $\Gamma_5$ are Archimedes Twin Circles. The triplet, $\Gamma_7$, was discovered in 1974 by Bankoff. Cut-the-Knot has a discussion of these circles.
Jan
21
comment Existence of a cyclic polygon with same sides as a given polygon
This answer might be helpful.
Jan
20
revised Geometry question about centroid
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Jan
20
comment Area Ratio of a Polygon
@problemsolver: It's still nice to know the source of a question, in order to get an indication of its difficulty or intended toolset. (Also, it's generally preferred that questioners provide context about their own attempts to solve their problems, so that we know how best to answer.)
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