So, the euler spiral! It’s the big one at the top. It’s traced out by the parametric equations wirtten under it.
I thought something interesting would happen if I replaced the cosine and the sine with the derivatives of the parameterizations of various other curves, and then this happened.
Came across this great book designer’s page http://retinart.net/graphic-design/secret-law-of-page-harmony/ via ilovecharts on Tumblr. It’s enthusiastic, detailed, lots of eye-popping illustrations. It’s about the best place to put content on a page.
Not only is there an excellent geometric method for producing this best text layout - for any proportion page - there’s a bevy of geometric claims about the result.
I thought it was fun, and started just because I wanted to see the layout for different shaped books. I’m a little too pleased with how it came out. Hope you like it.
“At the beginning of my teaching I was very content focused. I need to find and create interesting content that will help the kids, that the kids will be really interested in. I had no middling success with that. I think I found some great things, and also found some other things that didn’t work and I found that teaching some of the important ideas were harder than I thought they would be. I realized that there were plenty of ideas that I didn’t really understand myself, that I had to go back and think about a lot. I think going back and thinking about those ideas really helped me shift a little bit to not just caring about trying to find interesting content. But also thinking about pedagogy and how we teach things and the best ways for kids to learn. If I had to think of an arc of my teaching career and my focus, I would say that that kind of describes my arc of going from being very content-focused to a balance between finding interesting content and also really thinking about the best way for kids to learn the content and have an experience.” – Avery
Around 32:30-34:00 of Episode 105 of Infinite Tangents, Ashli @mythagon’s edunerd podcast.
Craig Winske made a nice sketch showing the mean dynamically and wanted some helping adding the median. Here’s his blogpost about it. I did that and a little guessing game, built on his nice structure.
Had way too much fun playing with this today.
#415 Hexagon morning – A new minimal geometric composition each
“Grown-ups never understand anything for themselves, and it is tiresome for children to be always and forever explaining things to them.”
— Antoine de Saint-Exupery
1. All beliefs in whatever realm are theories at some level. (Stephen Schneider)
2. Do not condemn the judgment of another because it differs from your own. You may both be wrong. (Dandemis)
3. Read not to contradict and confute; nor to believe and take for granted; nor to find talk and discourse; but to weigh and consider. (Francis Bacon)
4. Never fall in love with your hypothesis. (Peter Medawar)
5. It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories instead of theories to suit facts. (Arthur Conan Doyle)
6. A theory should not attempt to explain all the facts, because some of the facts are wrong. (Francis Crick)
7. The thing that doesn’t fit is the thing that is most interesting. (Richard Feynman)
8. To kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact. (Charles Darwin)
9. It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so. (Mark Twain)
10. Ignorance is preferable to error; and he is less remote from the truth who believes nothing, than he who believes what is wrong. (Thomas Jefferson)
11. All truth passes through three stages. First, it is ridiculed, second, it is violently opposed, and third, it is accepted as self-evident. (Arthur Schopenhauer)
Prospero’s Precepts – 11 rules for critical thinking from history’s great minds.
I’ll want to refer to these in the future.
Made a wee demonstration sketch to support beginning @GeoGebra animators.
Saw this beautiful rug at Islam and Art, and wanted to think about the tessellation. But one of the things I like about it is the inferred motion, so I tried to animate it, too. It’s a little clunky in GeoGebra because sooo many points are animated, but I’m pretty happy with the gif. Interestingly it’s smoother in the mobile (HTML5) version.
Geeky GeoGebra tidbit: I make the checkboxes affect each other using the SetValue command in the Scripting - On Update panel. Like SetValue[o,False] (or SetValue[α, 0°], or …) but this is the first sketch where I used a conditional. So If[!(o||s_1),SetValue[u_1,True]] turns on the u_1 textbook if both o and s_1 are off.