Cake is wonderful

who: J1 and J2
where: kitchen
when: afternoon during J3's nap
what material did we use: dish soap, water, a plastic drink bottle, zometool set, and two small blocks of solid CO₂

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Last weekend, a generous uncle brought two pieces of chocolate cake for the older J's (littlest J can't eat dairy, so has to make due with dark chocolate squares). The cake was nice, but the real delight was in two small pieces of dry ice that we part of the packaging to keep the cake cool. While J2 had his violin lesson, J1 and I looked for good activities to take advantage of this bounty.

We hit on the Crazy Russian Hacker's 8 dry ice activities (video linked below). Of those, we selected the smoke bubbles and the smoke rings since they seemed cool and possible with our resources. These turned out to be really easy and fun activities.

Here are some videos of the smoke rings:

By coincidence, our friend Pongskorn Saipetch was also playing with dry ice recently, you can see his video here. From the size of his piece of dry ice, I have to guess he had a lot of cake!


After the dry ice had melted, we made bubble wands out of zometool and continued to play with the soapy water:

Our video inspiration. While our photos and video didn't turn out this well, the actual experience was at least as much fun as what you see here:

Build a chair

who: J2
where: our reception room
when: after swimming lessons

NRICH has a simple activity: use unifix cubes to make a table and chairs. Here's the building material we were supposed to use:

We don't have these cubes at home, so we used TRIO blocks instead. These are 1x 1x n cuboids with a top and a bottom that can be connected. There are also sticks that can connect from any side of  and block to any other side of any other block. these sticks are either 3 or 4 units long.

Here is J1's chair:

After building the set, I asked what he thought of the challenge. He had to solve 2 problems in the construction:
(1) How to deal with the corners where he could only have one block connect to the leg
(2) how to connect the middle of the table so it wouldn't fall through the hole.

His answer was to use a two layer table with corner pieces in the two layers arranged orthogonally. For the middle of the table, he has some sticks along the bottom that support the unattached pieces in the middle (you can see a slight depression in the picture.

Finally, since he knows about the unifix cubes from school, we got to talk about how this construction would have been different using that building set. As always, this compare and contrast discussion was really good for getting him to think about the characteristics of the materials he was using..

Pseudosphere Hat and our Robot begins (some arts and crafts)

Who: J1
When: around lunchtime
where: on the floor

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Today, we tried making a couple of things. First up, was a pseudosphere.  The inspiration for this is a really nice post from Daniel Walsh: Sudo Make me a Pseudosphere. By all means go to the original post as the pictures, animations, and video he posted are far better than what we managed, but it was still a fun conversation about shapes, angles, slope, and fractions.

The process is easy:

1. cut out a bunch of equally sized circular discs
2. cut the discs into different sized (different angle) sectors
3. make all the pieces into cones
4. stack them from shallowest to steepest

Daniel mentioned something about calculating the optimal sizes, but I didn't really know what he meant. We went for a child's dinner plate for our circular template and cut sectors in multiples of 45 degrees.

Only the finest used newsprint for us!

One good question came up along the way: if I cut out a larger angle, will the cone we make be steeper or flatter?

Pseudosphere taking shape

There was another point where I'd cut out a 135 degree sector and J1 said: that's 1/3.  When he measured very roughly, it did seem to be a third, so I asked him to try it more precisely. He had a sudden realization when he saw the 90 degree remainder.

The cone of our dreams!

We went one step farther and permanently attached all the cones together, then re-purposed the whole thing to create 2015's fashion must-have item: the pseudo-rocket pseudosphere hat:

Starting our Robot

Our other activity is really the beginning of a longer project.. J1 has been talking about making a robot and we are starting to work on some of the main functions. Of course, he is really excited about camera eyes and a laser cannon, which we'll get to eventually (will we?) For now, I have some ideas about how to get the robot to walk.

My plan is to connect a basic rotating electric motor we have, so that leaves us solving an old problem: how to convert rotational motion into straight-line motion. Of course, wasteful methods are easy, but we want our robot to have the maximally powerful stride. For now, we are investigating multiple linkages, in the footsteps of Chebyshev.

Below is a first test: three linked arms:

1. Arm 1 has a fixed end and is intended to rotate in a circle
2. Arm 2 has one end fixed to the rotating end of arm 1. The other end of arm 2 is the motion we want to examine
3. Arm 3 has one end fixed and the other end attached to the mid-point of arm 2. This constrains that midpoint to travel along a circular arc

You can see our ultra-high tech implementation below, using card paper as the arms, a large cardboard box as the base, nails (into the base) to create fixed points, nails point up to create hinge joints, and extra bits of cardboard to cover the point ends of our hinges and past muster with  the health-and-safety inspectors:

The action of the multiple hinges is pretty wild. J1, J2, and I enjoyed cranking arm 1 and watching arm 2 fiddle around. Carefully holding a pencil in place, we managed to draw he path of arm 2's free end. It is the rounded wedge that looks very close to a circular quadrant.

If you want to see some great animations of multi-hinge contraptions, check out the animations at Mathematical Etudes. I'd be delighted if we could get close to this one.

Avocado update

I'm pleased to announce that another family member, D, has started sprouting her own avocado pit and, apparently, has made this into a race.  When told the news, J1 and J2 immediately started guessing what type of sabotage techniques would be employed by D. I think this says more about them than her.

Total mass: 67 grams
Length from root tip to sprout top: 21 cm
Length from pit to sprout top: 12.3 cm