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Space An Alternate Elective after Algebra II Henri Picciotto o MathEducation.page Math on Another Planet #1 A Long Month Evary Mo Tu We Th Fr Sa Su 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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Space

An Alternate Elective after Algebra II

Henri Picciotto

  • MathEducation.page
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Math on Another Planet

#1

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A Long Month

Evary Mo Tu We Th Fr Sa Su 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 …

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Isomorphism

+ d e f d + e e + f d + f d + e + f d e f d + e e + f d + f d + e + f

+ Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su

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Space: topics

  • Abstract algebra

◊ T

ransformational geometry

◊ Symmetry ◊ Dimension

  • 3D: polyhedra
  • 4D: introduction
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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

◊ T

ransformations: one-to-one functions (domain, range: the whole plane)

◊ Isometries:

transformations that preserve distance

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T ransformations Symmetry Dimension

Fundamental Theorem of Isometries: every isometry of the plane is a reflection, a rotation, a translation, or a glide reflection.

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T ransformations Symmetry Dimension

Computing transformations

using complex numbers:

◊ T

ranslation: add a+bi

◊ Rotation around the origin:

multiply by cos θ + i sin θ

◊ Rotation around (a,b): subtract a+bi,

rotate around the origin, add a+bi

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T ransformations Symmetry Dimension

Computing transformations using matrices

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

Handbook of Regular Patterns by Peter Stevens

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension

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T ransformations Symmetry Dimension: 3D

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◊ Platonic and Archimedean polyhedra ◊ Duality ◊ Euler’s and Descartes’ theorems ◊ Review of geometry and trigonometry

T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 3D

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T ransformations Symmetry Dimension: 4D

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T ransformations Symmetry Dimension: 4D

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T ransformations Symmetry Dimension: 4D

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T ransformations Symmetry Dimension: 4D

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T ransformations Symmetry Dimension: 4D

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T ransformations Symmetry Dimension: 4D

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Space

An Alternate Elective after Algebra II

Henri Picciotto The Urban School of San Francisco math-ed@picciotto.org www.picciotto.org/math-ed

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Space overview

Who takes the class Topics Review Resources Computer tools Juniors, before Calculus Seniors, instead of

  • r in addition to

Calculus

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Space overview

Who takes the class Topics Review Resources Computer tools Abstract algebra T ransformations Symmetry Dimension (3D, 4D)

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Space overview

Who takes the class Topics Review Resources Computer tools Algebra Geometry T rigonometry

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Space overview

Who takes the class Topics Review Resources Computer tools

Transformational Geometry by Richard Brown Algebra: Themes, T

  • ols, Concepts

by Anita W ah and Henri Picciotto Geometry Labs by Henri Picciotto Handbook of Regular Patterns by Peter Stevens Zome Geometry by George Hart and Henri Picciotto Flatland by Edwin Abbott

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Space overview

Who takes the class Topics Review Resources Computer tools Cabri II+ Cabri 3D (vZome)

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Space

An Alternate Elective after Algebra II

Henri Picciotto The Urban School of San Francisco math-ed@picciotto.org www.picciotto.org/math-ed

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Summer Workshops for Teachers

August 4-7 Grades 8-11: Visual Algebra August 10-11 Grades 11-12: No Limits!

Henri Picciotto Center for Innovative Teaching Urban School of San Francisco math-ed@picciotto.org www.picciotto.org/math-ed/cit