Show HN: Pi Explained Visually(setosa.io)
setosa.io
Show HN: Pi Explained Visually
http://setosa.io/ev/pi/
5 comments
Another approach: http://betterexplained.com/articles/prehistoric-calculus-dis...
The best way I've seen pi explained visually is pi-unrolled.gif: https://commons.m.wikimedia.org/wiki/File:Pi-unrolled-720.gi...
That is a great visualization but one something that bothered me about it was that you're constrained to watch it unravel at it's own playback speed.
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This would be a great resource for an advanced second grader.
I was recently thinking about defining things vs explaining them. When you're trying to understand something, I think it's easier to use a story like approach. "If you take the line making a circle (or circumference if you already know that one) and measure its length. Then you take the diameter…"
Once you know something, it's easier to shift that knowledge into a definition. "the ratio of a circle's diameter to its circumference." It's more concise and is more usable to tell subsequent stories and make subsequent definitions.
I think this might be a common mistake when explaining things. When we understand something, it's kind of stored as a stack of definitions. "Ratio between diameter and circumference" assumes the learner knows ratio, diameter and circumference. If they don't, the tendency is to build up their definitions. "Ratio is __. circumference is __. pi is__…" But definitions take a bit more effort to plug into your brain.
I think there's a programming paradigm analogy though I'm not quite fluent enough in the concepts to be confident about it. To venture.. a declarative programming's "Case Where" expression is more difficult to grasp than procedural "if then" if you're not familiar with conditionals in general.
I think this is why encyclopedias can be hard to understand. They kind of define things.
Once you know something, it's easier to shift that knowledge into a definition. "the ratio of a circle's diameter to its circumference." It's more concise and is more usable to tell subsequent stories and make subsequent definitions.
I think this might be a common mistake when explaining things. When we understand something, it's kind of stored as a stack of definitions. "Ratio between diameter and circumference" assumes the learner knows ratio, diameter and circumference. If they don't, the tendency is to build up their definitions. "Ratio is __. circumference is __. pi is__…" But definitions take a bit more effort to plug into your brain.
I think there's a programming paradigm analogy though I'm not quite fluent enough in the concepts to be confident about it. To venture.. a declarative programming's "Case Where" expression is more difficult to grasp than procedural "if then" if you're not familiar with conditionals in general.
I think this is why encyclopedias can be hard to understand. They kind of define things.