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References and Further Readings

Page history last edited by Jonathan Dietz 8 years, 1 month 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:

 

 

Group Theory

 

 

 

 

 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:

 

 

Geometry of Soap 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

 

 

 
 

 

 

 

 

 

 

Fractal Geometry

 


 

 

 

 

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/    

 

 

Arthur Fiedler Memorial  by Ralph Helmick

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