The mathematician formerly known as DayLateDon

2d
revised How to determine the side on which a point lies?
added 62 characters in body
2d
answered How to determine the side on which a point lies?
2d
awarded Editor
2d
revised A community blog for Math.SE
added 94 characters in body
2d
revised A community blog for Math.SE
added 94 characters in body
2d
revised A community blog for Math.SE
added 94 characters in body
2d
comment What is the proof of $\cosh{x}=\frac{e^x+e^{-x}}{2}$?
@solstafir: You can define $\cosh$ and $\sinh$ based on an arc-length parameter (your $z$); however, hyperbolic arc-length cannot be expressed in terms of elementary functions. (Lengths of curves are almost-always trickier to calculate than the areas they bound; circles (& lines) are the primary exceptions.) The length of arc $V^\prime P^\prime$ involves $\int \sqrt{1+x^4}/x^2 dx$, which is quite non-trivial, so hyperbolic trig values would effectively be "non-arithmetical" functions of an arc-length-based angle measure. It's certainly not the case that arc-length is twice the sector area.
2d
awarded calculus
2d
answered What is the proof of $\cosh{x}=\frac{e^x+e^{-x}}{2}$?
2d
comment What is the proof of $\cosh{x}=\frac{e^x+e^{-x}}{2}$?
@SanathDevalapurkar: One can define $\cosh u$ and $\sinh u$ geometrically as hyperbolic analogues of $\cos\theta$ and $\sin\theta$, taking $(\cosh u, \sinh u)$ to be points on the "unit hyperbola", $x^2 - y^2 = 1$. In that case, the relation between these values and exponentials does require proof. (I may have posted one on MSE at some point.)
Apr
16
revised Geometry, Find sides of a triangle
added 24 characters in body
Apr
16
comment Finding circumcentre
¡H$\large{⊍}$ZZ$\large{⩀}$H!
Apr
15
comment Prove that this triangle is equilateral?
@user143201: $\triangle ABD$ is a right triangle whose hypotenuse is twice as long as one of its legs. That only happens for $30^\circ$-$60^\circ$-$90^\circ$ triangles. :)
Apr
15
answered Finding circumcentre
Apr
15
answered Locus of Point P
Apr
15
answered Prove that this triangle is equilateral?
Apr
14
comment Use of "I" in mathematics papers
@user1577636: Perhaps if you post the abstract, we can offer more-specific advice. By the way, you might also browse Academia.SE; for instance, "What to use instead of academic 'we' when describing an experiment?".
Apr
14
comment Use of "I" in mathematics papers
Come to think of style guides: "Mathematical Writing" by Knuth is a worthwhile (and free!) read. The sixth "especially important" point (page 2) addresses the use of "we", stating that "[The usage] is not a formal equivalent of 'I'.".
Apr
14
comment Use of "I" in mathematics papers
I try to reserve "we/us" to indicate "myself, and you, the reader, who joins me on this intellectual adventure", in constructions like "We take $\alpha$ to be ..." or "Let us embed the figure in $n$-dimensional space ..."; mixing that usage with the Royal We can be a little confusing (but I don't believe it's too big of a deal). You can always use "this author" to signify your specific contribution, with @Gerry's suggestion to get it out of the way early: "The following discusses this author's research into (whatever)...". In any case ... Doesn't the competition suggest a style guide?
Apr
14
answered Volume of a parallelpiped from its sides and diagonals?
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