A review of Over / Under by Gamewright

I was walking my dog last week and ran into a math / education professor I know in the local conservation land. When we chatted about the holidays he mentioned that his family played a game called “Over / Under” and loved it. I ordered it as soon as I got home 🙂

Here’s our quick review of the game which looks like a really fun game to play with kids.

(1) The unboxing:

(2) Next – one quick round of the game (which we didn’t play quite right, but you’ll get the idea):

(3) Finally – a few thoughts about the game and then a round that we made up 🙂

I really like the idea behind the game and can’t wait to play it a bit more.

As an aside – we’ve reviewed two other games by Gamewright that we love 🙂

A review of On the Dot by Gamewright

A review of Terzetto by Gamewright

Images of a 4d sphere intersecting a 3d cone

For our Family Math project today we played with the idea of a spheres intersecting objects other than a plane. The idea was to explore how a 2d being on a cone, say, would “see” and describe a sphere passing through the cone. That project is here:

What if Flatland wasn’t a plane

Tonight I revisited the project just to see the different images of a 4d sphere intersecting a 3d cone. I wanted to see the analogous and presumably not really spherical shapes.

Here are some pictures.

(1) A 3d sphere intersecting a 2d cone as it descends down the middle of the cone:


(2a) The analogous picture of a 4d sphere intersecting a 3d cone:


(2b) Note the intersection does have a hole in the middle:


(3) Now I shift the sphere so that it is descending down the cone slightly off center. For the 3d sphere intersecting the 2d cone you get this picture:


(4) And here’s the same situation with a 4d sphere intersecting a 3d cone:


It is fun to see and try to imagine these images. The usual way of thinking about constructing a sphere (either 3d or 4d) makes some sense when you think about stacking up the images of the intersection with a 2d plane or with 3d Euclidean space. Trying to “stack” the images if the sphere intersecting the cone to make either a 3d or 4d sphere is really not intuitive for me at all!