Math + Making

A student blog for Math 189AH: Making Mathematics at Harvey Mudd College

flowers and bubbles !

Nora O’Connor
Mehak Garg

we made surface-minimizing bubbles and also added some more to our penrose tiling! Neither project had a huge learning curve, but it was fun to learn about a new math concept and do tactile things!

first flowers

Nora introduced me to the topic of Penrose tilings and I thought the math behind them was super cool. Specifically, I was reading this paper and it was cool learning about other tilings that rely on this aperiodic nature and things like the “Penrose staircase”.

a Penrose staircase!

Nora gave me one of her Penrose tilings that was in progress and we scavenged for some leaves and flower petals. We ended up also finding some of her older leaves and flowers so we got to experiment with fresh flower petals and older ones too! She gave me a wooden stencil for how to cut out the leaves and petals and an exacto knife to cut them out.

Here are some of our materials:

Initially, I really struggled to cut the dry leaves since they were so brittle and I messed up quite a few leaves. The learning curve to cutting was steeper than I thought.

We struggled initially to get fresh materials because it had been raining that day and so our flowers and leaves were all very wet. When Nora first did this project, they were able to get dry materials and then let them dry further for a day but we were not able to do that so we tried patting them dry the same day.

The wetness of the fresh flowers made them slightly harder to cut so we ended up using some of Nora’s older materials to cut out of the petals! However, the older leaves ended up being quite brittle so we ended up using the fresh leaves we plucked that day.

Nora and I traded between cutting shapes and gluing them down and started to add on to the existing tiling. We used a reference photo for the Penrose tiling to build onto the image but…

we totally made a mistake on this (can you spot it…)

With this final product, what’s cool is that you can see where we started to use newer leaves in comparison to the older materials!

now bubbles !

mehak first taught me about minimal surfaces! apparently, bubbles will like always make one which is pretty cool! I played with the dish soap and built some shapes but we were kinda rushed for time while together.

i was just in my room chillin’ the next day and I spotted my dish soap and molecular model kit and thought it might be silly to make some more bubbles

its a bit hard to see here but i got it to make like three connected ones? anyway -pretty fun tactile project. i dream that one day we will develop the technology to blow square bubbles, but until then they can continue surface minimizing away…

i also was googling and found these cool papers:

woah! my personal challenge for this class has been to try to find a relevant chemistry thing for every new math concept i learn because i want to find ways to keep doing math even tho its not my major! for the penrose tiling i found some cool stuff abt penrose nanotiles and chemical tesselations which is a little related to the paper mehak linked!


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