#practical math

I quickly grabbed 12 tiny strips of foil with holes in their ends, 6 screwable rivets, and a lanyard - and built an octahedron net I can carry around my neck.

The chance I might lose the icosadron model/ "inlay" is a bit higher as with my other plastic foil and rivet constructions - as - if I lose one rivet the hole in this net is large enough for the icosahedron inlay to fall through. (The rivets are just screwed in - so I can also take the inlay icosahedron model out. ). And losing one rivet is very probable.

But I take the risk - as I would most certainly notice the colorful icosahedron falling down if I lose a rivet. (The tiny rivet would most certainly be lost...But that loss is rather unimportant.)

- - -- --- -----

Side thoughts:

I love how such strips-and-rivets models are helpful for visualizing graph networks.

The rivets are nodes.

The strips are edges.

-> Also:

[Sorry for the incoming word salad/ thought gibberish:]

The stability of the physical models is better the more connections(/strips/edges) exist between the rivets/nodes. (More connections per rivet and more stability go hand in hand - literally. Losing one rivet/node would have less impact on the overall stability the more connected all rivets/nodes are towards each other.)

[ Further thoughts: Similar principles exist in the memory and how more connected memories are less prone to be forgotten. This is often the case for the learning technic of "Eselsbrücken" - i dont know the english equivalent rn- it means using associations to memorize stuff more easily - so it sticks better in the memory. (I might add an example later. But am too lazy rn)

Memory works like a dynamical graph network... ]

The printer only prints 20 pages at a time. A student wants to print a PDF with 128 pages but to save money, combine 6 pages on each page. How many of the 128 pages should you then print so the output is exactly 20 pages?

Hint: 128 pages of the PDF printed this way equals 22 pages.

I used to love algebra in school. I was a math nerd. But I am badly out of practice. Anyway I did manage to figure it out and printed 1-120 and then 121-128 in this compressed mode. But I had to do it by trial and error coz my brain wasn’t mathing. If I had some paper I could have written down:

128/6 = 21.333 rounded up to 22; 22-20 is obviously 2 and 2 x 6 is 12 uh

Progress continues, slowed a little by my dealing with a migraine that took me down this morning. We didn’t really get going until afternoon, and by then it was already more than 100F out there. Slowly, slowly. Patience, and lots of liquid, and then my friend handing me about 32 oz of delicious iced coffee while we sat watching my son mow & mulch and we chatted.  The main cut made, now he’s got…

It took me a minute to realize what this was. 

It's a math equation in visual form. 

A²+B²=C².  The short side is A, the mid-length one is B, and the long one is C.  When both A and B are multiplied by themselves and added together, they exactly equal the amount of C multiplied by itself. 

I learned this equation in school, and I occasionally use it at work.  I've been familiar with it for years. 

But this is the first time I've ever been able to see it.  Now I actually understand why it works!