bob012345's latest activity

Same shape in this context means that they overlap, they are the same size and thus are identical so that is not a valid solution as I...

Yes.

Identical here means they have the same shape. Think of it like two pieces of physical paper. Only the shapes matter.

Here is a little puzzle from Pierre Berloquin’s book 100 Geometric Games. The goal is to cut the figure once to make two identical...

I think the bigger issue is if the orbit of the rod itself is stable. Of the five LaGrange points in the Earth-Moon system, two are...

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...