bob012345's latest activity

Here is a schematic of the puzzle. So, my solution is translate BC northeast by a small amount transate DE southeast by a small...

I like old stuff from the 60’s like ‘Eight Miles High’ by the Byrds. Commercial jets usually fly six to seven miles high but on a recent...

Another solution F is on AC. ##\angle ACD = \pi/4## ##\angle AOD=\pi/2## ##\triangle AEO \equiv \triangle OGD## ##EO=GD## Thus...

Here is my proof. $$r_1^2+(r_1+d)^2=R^2=r_2^2+(r_2-d)^2$$ Solving for ##d##$$d=\frac{r_2^2-r_1^2}{r_2+r_1}=r_2-r_1$$ Therefore...

No, that is not my proof, just an observation.

The extreme cases I mentioned are when the radius of the smaller semi-circle goes to zero, the larger semi-circle fills exactly half the...

NOT ELEGANT solution The eqation of the circles $$x^2+y^2=R^2$$ $$(x-x_1)^2+y^2=R^2-x_1^2$$ $$(x-x_2)^2+y^2=R^2-x_2^2$$ By subtraction...

Here is a puzzle from Catriona Shearer. Find the area ratio of the shaded semi-circles to the circle which they fit in. The bases of the...

Also, the minimum age for Ivy such that Holly is alive 15 years ago is 19.5 years old.

We don’t have enough information to calculate the ages of Holly and Ivy but we can determine the relationship between them. Using the...

I think there is a bit more to explore to this problem. For example, what is the current relationship between the ages of Holly and Ivy...

That is until someone falls into a black hole and gets spaghettified.

Suppose any two volumes with one properly contained within the other. As the number of dimensions increases the relative volume of the...

Ah yes, of course - obvious once you point it out.

Possibly related and interesting: 3Blue1Brown (YouTube) - Thinking outside the 10-dimensional box 3Blue1Brown (YouTube) - The most...