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Math Projects in Scratch : Primes, Codes, Counting, Geometry
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Название: Math Projects in Scratch : Primes, Codes, Counting, Geometry
Автор: Michael Mays
Издательство: Leanpub
Год: 2022-08-31
Страниц: 187
Язык: английский
Формат: pdf (true), epub
Размер: 30.4 MB

What can you do with Scratch besides write games? Lots of math projects, secret codes, the geometry of Pi, Fibonacci numbers, prime numbers, and other sequences, and more!

One story in Frederik Pohl’s anthology Star Science Fiction # 4 is by Fritz Leiber, about a supergenius kitten named Gummitch who planned to write books explaining the world to other genius kittens. One book was to be “Space-Time for Springers,” and that is also the title of the story. My mathematical research is in number theory and combinatorics, often aided by computer explorations. Now I have grandchildren at the age of enthusiasm and wonder, one of whom introduced me to the computer language Scratch. The mascot of Scratch is a smiling ginger kitten, who might as well be Gummitch. This book uses Scratch to develop some ideas in mathematics and to invite exploration, written with my grandchildren in mind. The title I chose makes clear the subject (mathematics) and the tool for exploration (Scratch), but in spirit I tried to write the book Gummitch would have wanted: “Numbers for Springers.”

The aim is to keep the mathematical level of this book so that it relies at most on algebra and geometry. Even that might be a stretch for elementary school students, but there is an art to stretching without breaking that every supergenius kitten comes to know.

Exploring a computer language involves seeing what it can do, figuring out how the questions it can answer intersect with the questions we want to answer. Of course a computer is a universal machine, so as long as it is Turing complete the programming language doesn’t matter: if the question has a computable answer, pretty much any language will do. But languages are designed to have certain strengths, and the underlying structure of the language can encourage more or less productive habits of thought. Think of the spaghetti code encouraged by GO TO statements in BASIC or FORTRAN, or the promise of organization and reuse in object oriented languages. Scratch is a language that encourages play, optimized for graphics, sound, and games, so it is worthwhile to channel its spirit of play into realms beyond. This book is not a mathematics text, and it does not aim to provide a theorem-proof development of mathematical topics. Instead, it presents ideas from mathematics such as number representations, divisibility, prime numbers, and cryptography that have immediate application and are fun to code. It highlights efficiency of algorithms in a way to demonstrate how a little forethought can make computations accessible that otherwise would be time-and-resource constrained. It is a primer, a first book for learning about properties of numbers and other mathematical objects, about how to ask interesting questions, and how to use a computer to answer them.

Scratch encourages collaboration and sharing, and in that spirit all the programs in this book are on the Scratch site at the Numbers for Springers studio.

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