bob012345's latest activity

Expanding the original problem to be an ## nx1## rectangle, it turns out the angle B to add to angle A (defined by the ratio...

One can take the log of both side of the inequality and plot that. That plot looks identical but goes on exponentially further. The...

Demos is the greatest of all time calculator. Used it a bit in high school over a decade ago, and it helped me visualize math concepts.

The plot can also be generated easily on Desmos.

I noticed the following question generated quite a lot of interest on the Internet. Which is larger ##e^{\pi}## or ##\pi^e##? Most (if...

Here is a plot of the region where ##a^b>b^a## I think your rule covers the upper right and lower left quadrants. (the quadrant lines...

It can be shown that the yellow figure of the last graphic in post #8 can be completely contained in the blue figure. Take off an...

Graphing gives a visual answer but doesn't really prove anything. Let AO be area of the circles = pi x r^2 Let AT be area of the...

I finished - and printed - my collection of short stories! There Be Monsters A collection of fantastical maritime-themed short stories...

The equation ## C=A+B ## is actually Euler's formula $$ \arctan\frac12+\arctan\frac13=\frac\pi4 $$, and there are three more formulas of...

Here is another way but it’s just a variation of @coquelicot above in post #7 but the lengths are not obvious so they must be...

Based on the previous posts, it can also be shown that A+B+C=D for the angles A, B, C, and D in the next picture. Or A+B+C+D=E for...

The solution below is not mine – I saw it on YouTube, here. This is just my summary. 1. Add 3 squares and consider the triangle...

Just another approach: