Nov 6, 2023
Polyhedron cards
seen from Singapore
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Polyhedron cards
That stim toy is also a 'calculation rag' for some binary number stuff...
Everything can be used as a calculator...
... plus, this 'calculator rag' feels nice!
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... You can even turn it around and have a kind of invert thing.
hmm.. I wonder what sort of useless things I come up with as I add some transformation concepts in this calculator rag thingy.
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This stim toy might be a nice tool for explaining some binary number system stuff and arithmetics to people/children in a more playful, interactive and enjoyable way.
Tiny hexagon-spiral booklet with friend-shaped friend shapes of joy (platonic and archimedean solids drawn in isometric projection)
Front- and backside:
Laying at a stone to make the hexagon-spiral booklet appear more plastic:
This booklet can be folded into a tiny hexagon with moderate thickness:
New challenge (to establish a daily routine): Creating one new polytope info card after breakfast - each day.
(That is the first page of the list of the polytopes I want to make. (92 Johnson solids will be very very much, and I have to stop myself from thinking about those many solids. but eeeh. we might approach it step by step... )
So, I started the polytope cards project some time in the summer of this year.
I already made all 5 platonic solids,
some regular 4-polytopes (the 4D platonic solids plus the 24-cell that has no 3D sibling),
and the first 4 archimedian solids.
Today I created the truncated octahedron card:
Yesterday I made the truncated tetrahedron card:
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The general template of the cards is as following:
This project is still in progress.
Furtherly I want to add:
General explanations/index cards/summaries
Polytope info card of the Snub Cube
Today's shape was the archimedian solid "Snub cube".
The snub cube has 38 faces in total - 6 square faces and 32 triangular faces.
It has 60 edges and 24 vertices.
Each vertex is met by 4 triangle faces and 1 square face.
A snub cube is an alteration of a truncated cuboctahedron.
The drawing:
For the isometric projection drawing I started with a truncated cuboctahedron, and continued to alter the truncated cuboctahedron's octagonal faces into square faces.
"The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head."
G.K. Chesterton
Euler's Identity and the 3D unit helix
Sine and cosine are the 2D projections of the unit helix.
When I first saw the concept of the unit helix some years ago, trigonometric functions made so much sense.
Unfortunately, I never heard of any of it in school. Trigonometry was taught as a very unintuitive thing, as something one could not have a connection towards, as something not really 'integratable' into one's own mind. There were no elaborations about 'why' equations are the way they are, nor how the methods are used in relation to the "why", and what these methods are in concrete - in a manner which can be plotted in one's own imagination.
The abstraction appeared alienated from the own thinking process. No inner comprehension was really possible.
Yet, seeing only this concept with no further words added, it was an "Eureka-moment" for me.
In my opinion, Euler's Identity deserves the status of the most elegant and beautiful equation.
[Picture ID: Facebook comment by Mason:
What I hate is that when I say I study mathematics I usually only get two responses:
1) "Oh! You must be very smart!" which is annoying because I don't consider myself intelligent just because I'm good at one subject. I also don't like to have my ego inflated, and responses like that don't help.
2) "Oh! I hate math!" which is just a stupid thing to say about a subject after your told that it is someone's livelihood.
On the off chance that someone actually says, "Oh! That's cool, what do you study specifically?" The question inevitably comes to "How is that useful?" since so many people have been taught since elementary school that math MUST have applications or it's not worth studying. I've only found two or three people who make it that point of the conversation and genuinely find interest in the topic, and one of them is my wife lol!
Long story short, mathematics is a lonely field, which is hard when you love talking about it.
]