Math goggles: tasty sphere packing around the world
Math goggles help you notice math everywhere. Maria João Lagarto has great math goggles when she makes adventurous Pinterest collections. For this post, I selected examples of round fruits, confections, and other morsels packed into triangles, pyramids, or cones. Even the Wikipedia article on sphere packing uses a pyramid of oranges!
I used to play with a few beads of caviar as a kid, back in Ukraine. Red caviar is a great plaything because of the weird texture and beautiful translucency. But I’ve never managed to build a pyramid. Check out this caviar-inspired, one-paragraph review of 400 years of the history of sphere packing at fotomat.es.
Meanwhile, across the world – in Thailand – there is an annual celebration with an awesome name: Monkey Buffet Festival. It features giant pyramids of fruit for monkeys to enjoy. Yes, monkeys know how to drink out of cans.
They also build giant fruit pyramids in India. This photo is from the All India Mango Festival.
Meanwhile, Europe stacks its chocolates into cones or pyramids:
And Americans play with cereal and pie.
Play with your food – pack some spheres!
Posted in Grow
Also billiard balls in a triangular frame and in a square box. http://previewcf.turbosquid.com/Preview/2014/07/08__14_45_55/6.jpg5882454d-c421-4896-ae99-f6fc38e7cc47Large.jpg
http://www.museumofplay.org/blog/play-stuff/wp-content/uploads/2009/12/10915134.jpg
it’s easy to see which way of arranging them is more compact!
To uphold the edible theme let’s substitute the pool balls with eggs. How come egg cartoons are rectangular as opposed to triangular or hexagonal? Would it optimize space if they were shaped differently? what if you had to pack them into a parallelogram truck or stack them onto a rectangular shelf?
What a cool idea! I did a web search on “triangular egg cartons” and found quite a lot of intriguing images. Package design is a thriving industry, with a lot of people reinventing wheels and boxes. This collection has a cool name: http://www.beachpackagingdesign.com/wp/2013/04/4-extremely-polyhedral-egg-cartons.html
The website is pure awesomeness!
We did what you suggested and packed some spheres. Apparently if you fill a container with cherries it is heavier than if you fill it with apples. and it takes fewer cups of water to fill it up while washing the fruit!
And then I totally lost my 1-year old to cherries.
Sounds… sweet!
Olga, do you have any pictures of your packing adventures? Love the explorations: easy, but complex.
Unfortunately, we didn’t take pictures that time. But we’ve just integrated a couple of potatoes and this time we took a few.
Turns out, if you cut it into 16 pieces you get three types of fries out of one potato:
http://ic.pics.livejournal.com/olgayaroslavna/6311585/116120/116120_600.jpg
http://ic.pics.livejournal.com/olgayaroslavna/6311585/116766/116766_600.jpg
http://ic.pics.livejournal.com/olgayaroslavna/6311585/116721/116721_600.jpg
http://ic.pics.livejournal.com/olgayaroslavna/6311585/115738/115738_600.jpg
http://ic.pics.livejournal.com/olgayaroslavna/6311585/116319/116319_600.jpg
Then we tossed the potatoes with some herbs and oil and baked them :)
What a neat story! Potato pieces make nice play things, because they are hard enough and edible enough. Thank you for the photos. I want to post them separately, when we make a series of parent stories for September 25 Math Storytelling Day celebration.
Sounds great! We’ll be looking forward to the series. Finding edible math is a lot of fun when you have a toddler – so you can have your pi and eat it too!