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References and Further Readings

Page history last edited by Jonathan Dietz 10 years, 11 months ago

Euclid Online:

http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

An Introduction to the Works of Euclid http://www.obkb.com/dcljr/euclid.html

Historical Background for Euclidean Geometry:

Introduction to Euclid as the Father of Geometry

http://www.khanacademy.org/math/geometry/intro-to-euclidean-geo/v/euclid-as-the-father-of-geometry ( Video)

Active Geometry: The House that Euclid Built

http://youtu.be/no09CQGrFiQ

Carl Sagan Cosmos- Eratosthenes

http://youtu.be/bpp7i5bYLxI

Eratosthenes (the details)

http://youtu.be/rIF6Vj6pVNg

Agora (movie about Hypatia of Alexandria)

http://youtu.be/39l11Hw-jrk

Geometry and Architecture:

Henry Skupniewicz, MIT Department of Architecture
Architecture and Geometry
Sketches of Frank Gehry: http://youtu.be/O6TAs2WptEA
Sacred Geometry( Wikipedia) http://en.wikipedia.org/wiki/Sacred_geometry
Gothic Geometry http://www.newyorkcarver.com/geometry/geometry.htm

Group Theory

Textbook on Groups-Part I
Textbook on Groups- Part II

Video: Singing Banana's Introduction to Group Theory http://youtu.be/ylAXYqgbp4M
Numberphile on Rubik's Cube http://youtu.be/QV9k6dRQQe4
An Introduction to Groups: http://www.mathsisfun.com/sets/groups-introduction.html
Plus Maths.org: Group Theory http://plus.maths.org/content/teacher-package-group-theory
Getting to know groups http://plus.maths.org/content/os/issue39/features/colva/index
Rubik's Cube in 26 Steps http://plus.maths.org/content/os/latestnews/may-aug07/rubik/index
Symmetry: Through the Looking Glass http://plus.maths.org/content/os/issue24/features/symmetry/index

Discrete Math- Prof. Javed Aslam

Math Aside: Binary Arithmetic

Notes on Transistors and Logic Gates

Boolean Algebra

DeMorgan's Theorem

Algorithms

Discrete Structures Textbook(Complete)

Geometry and Fiction:

And He Built a Crooked House by Robert Heinlein (story)
A Subway called Moebius by AJ Deutsch
The Devil and Simon Flagg

Geometry of Soap Bubbles

Geometry of Soap Bubbles
Exploratorium: When Bubbles Meet Bubbles
The Shape of Bubbles

Mathematical Art:

The Geometry Playground from the Exploratorium

http://www.exploratorium.edu/geometryplayground/

STL (Stereolithography) File Format

http://en.wikipedia.org/wiki/STL_(file_format)

STL files describe only the surface geometry of a three dimensional object without any representation of color, texture or other common CAD model attributes.

An STL file describes a raw unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system.

SVG ( Scalable Vector Graphics) File Format

http://en.wikipedia.org/wiki/SVG

Scalable Vector Graphics (SVG) is a family of specifications of an XML-based file format for two-dimensional vector graphics, both static and dynamic (i.e., interactive or animated). The SVG specification is an open standard that has been under development by the World Wide Web Consortium (W3C) since 1999.

Bezier Curves

http://en.wikipedia.org/wiki/B%C3%A9zier_curve

Lasercutter Tutorials ( AS 220 Labs)

http://www.as220.org/labs/fabacademy/tutorials/using_epilog_laser.html

Lasercut Architectural Model

Sticks,Inc. Handpainted Furniture by Sarah Grant

http://www.sweetheartgallery.com/sticks-furniture-and-object-art.html

Tangrams/Geometric Puzzles

http://pbskids.org/sagwa/games/tangrams/

Fractal Geometry

Fractals http://mathworld.wolfram.com/Fractal.html

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.

Fractals for School http://math.rice.edu/~lanius/frac/

Golden Rectangles

Design Thinking:

We welcome our students with a methodology for innovation that combines creative and analytical approaches, and requires collaboration across disciplines. This process—which has been called design thinking—draws on methods from engineering and design, and combines them with ideas from the arts, tools from the social sciences, and insights from the business world.

At the d.school, we learn by doing. We don’t just ask our students to solve a problem, we ask them to define what the problem is. Students start in the field, where they develop empathy for people they design for, uncovering real human needs they want to address. They then iterate to develop an unexpected range of possible solutions, and create rough prototypes to take back out into the field and test with real people. Our bias is toward action, followed by reflection on personal discoveries about process. Experience is measured by iteration: students run through as many cycles as they possibly can on any project. Each cycle brings stronger insights and more unexpected solutions.

Methods: http://dschool.stanford.edu/use-our-methods/

Standards:

Massachusetts Current Frameworks

http://www.doe.mass.edu/frameworks/current.html

NCTM Geometry Standards

http://www.nctm.org/standards/content.aspx?id=314

Next Generation Science Standards

http://www.nextgenscience.org/