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Turtle Geometry: The Computer as a Medium for Exploring Mathematics (Artificial Intelligence)

Harold Abelson, Andrea Disessa · 6 HN comments
HN Books has aggregated all Hacker News stories and comments that mention "Turtle Geometry: The Computer as a Medium for Exploring Mathematics (Artificial Intelligence)" by Harold Abelson, Andrea Disessa.
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Amazon Summary
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen. The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates.
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The book Turtle Geometry [1] by Harold Abelson of SICP fame is a pretty cool exploration of mathematics all the way up to non-euclidean geometry using turtle graphics.

[1] https://www.amazon.com/Turtle-Geometry-Mathematics-Artificia...

My favorite Logo-for-relative-grownups work is https://www.amazon.com/Turtle-Geometry-Mathematics-Artificia... -- yes, with the same coauthor as SICP. It's about math more than CS, and it's really good: by the last chapter you're figuring out motion in general relativity. It has a spirit of DIY exploration unlike any other math book I'd seen at the time.
Something more than a weekend splurge:

Turtle Geometry: The Computer as a Medium for Exploring Mathematics

http://www.amazon.com/Turtle-Geometry-Mathematics-Artificial...

...and I've not yet tried it, but netlogo sounds interesting.

https://ccl.northwestern.edu/netlogo/

voltagex_
Offtopic: That netlogo site presents what appears to be an Internet2 cert signed by "InCommon RSA Server CA". It's untrusted by Firefox 45.0.2.
voltagex_
Turtle Geometry book as a "borrowable" ePub (DRM). https://openlibrary.org/works/OL3267302W/Turtle_geometry
Apr 07, 2014 · vinalia on Teaching Devina to Code
It might be fun to look at LOGO (maybe UCBLogo[1], free books included) for a first programming language. This has a first-person (turtle) view on a GUI that you move around to make shapes and do math/physics. The idea is that when programming it will be easier for the programmer to associate themselves with the turtle and interaction/exploration in the language will be natural.

The Logo way is pretty different from conventional programming models because it was tailored to be more intuitive than conventional languages like C, JavaScript, or VB. It still offers access to complex, higher order programming concepts like algorithms, AI, automata, etc. Harold Abelson from MIT (SICP) wrote a cool book that covers math/physics in Logo, too.[2]

The creator of the language has an awesome book[3] on how computers can enhance pedagogy and someone wrote a cool blog post on programming for children that mentioned it too[4].

[1] http://www.cs.berkeley.edu/~bh/logo.html

[2] http://www.amazon.com/Turtle-Geometry-Mathematics-Artificial...

[3] http://www.amazon.com/Mindstorms-Children-Computers-Powerful...

[4] http://worrydream.com/LearnableProgramming/

Apr 07, 2013 · sea6ear on Spirograph in HTML 5
I find Hal Abelson's book Turtle Geometry [1] fascinating. It describes a dialect of Logo (the graphical routines could probably be implemented relatively easily in Python/Tkinter or Tcl/Tk or something like Processing).

Once the basics are described, then it uses them to go on to explore things like non-euclidian geometry (and maybe topology?).

[1] http://www.amazon.com/Turtle-Geometry-Mathematics-Artificial...

Learning to build or repair a car would probably improve your understanding of thermodynamics, aerodynamics, momentum, etc. Likewise, writing a computer program that simulates the motion of a planet around a star or renders 3D graphics might improve your understanding of classical mechanics and any number of topics in math, just to name a few examples; cf.

http://www.amazon.com/Mindstorms-Children-Computers-Powerful...

http://www.amazon.com/Structure-Interpretation-Classical-Mec...

http://www.amazon.com/Turtle-Geometry-Mathematics-Artificial...

This is not to mention that learning how to program a computer is just another tool to put in your bags of tricks for solving problems in any of the domains you mentioned (some better suited than others, of course).

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