January 2013. In order to read the updated and more complete version of this post click here:Parashah VaEra and Bo “Every first-born in Egypt will die...”

[Please read the essential constructs in the right column. They provide the information necessary to understand the posts. If you are new to this blog, you may wish to start with the earliest post to see the progression in the sequence of events] VaEra and Bo will be combined because they both deal with the plagues in Egypt.

Pharaoh was the great pretender. The next warning however is somewhat different in that Moses went to Pharaoh directly in his home in order to provide him with warning. The third "warning” was still different, in that there was no warning for the coming plague at all. In these first 3 plagues we see a pattern. The 4th, 5th and 6th plague repeat the same pattern. As you might suspect, this pattern continues through the next set of plagues. Interesting pattern! FRACTAL Sequencing and animation MACHINE. The shape you see is the combined output of the controls below.

Mouse over them to see what they do. If the page gets too slow, turn some of the parameters down. Press H or ~ to hide the controls. Hyperbolic Orthogonal Dodecahedral Honeycomb. Geometry Expressions. George W. Hart. Slide-Together Geometric Constructions. This is a web version of a teacher's workshop presented at Bridges 2004Appeared in: Bridges for Teachers, Teachers for Bridges, 2004 Workshop Book, Mara Alagic and Reza Sarhangi eds., pp. 31-42.

“Slide-Together” Geometric Paper Constructions George W. Hart Computer Science Dept. Stony Brook University george@georgehart.com Abstract Seven paper construction projects provide students with experience exploring properties and relationships of two-dimensional and three-dimensional geometric figures. “Slide-togethers” based on squares, triangles, pentagons, and decagons Introduction This activity consists of seven attractive constructions which are fun and relatively easy to make because one simply cuts out paper pieces and slides them together. Each “slide-together” is made from identical copies of a single type of regular polygon (e.g., just squares or just triangles) with slits cut at the proper locations. “Slide-togethers” based on hexagons, decagrams, and pentagrams Copy and Cut. References. A First Course in Linear Algebra (A Free Textbook)

Open-Source Textbooks Instead I am concentrating recommendations and examples within the undergraduate mathematics curriculum, so please visit the Open Math Curriculum page.

If you are linking to this site, please use that page for a broad list, or link to linear.pugetsound.edu specifically for the Linear Algebra text. Thanks for your help publicizing open textbooks. This page contains some links to similar open-source textbooks. Notice however that a book that is free to download, but with a copyright that reserves the author's rights, is not really free. Free Textbooks Abstract Algebra: Theory and Applications, by Thomas W. Freedom Some thoughts on open-content, intellectual property, open-source software and books.The Economy of Ideas An essay on intellectual property, copyright and digital media.

Sources of Open-Content Textbook Revolution Careful capsule descriptions of free textbooks in many disciplines. Harmonograph. A harmonograph output A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image.

The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890s, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.[1] A simple, so-called "lateral" harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface.

One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. A particular type of harmonograph, a pintograph, is based on the relative motion of two rotating disks, as illustrated in the links below. Computer-generated harmonograph figure[edit] in which represents frequency, represent phase, The KnotPlot Site. What's Special About This Number? What's Special About This Number?

If you know a distinctive fact about a number not listed here, please e-mail me. primes graphs digits sums of powers bases combinatorics powers/polygonal Fibonacci geometry repdigits algebra perfect/amicable pandigital matrices divisors games/puzzles 0 is the additive identity . 1 is the multiplicative identity . 2 is the only even prime . 3 is the number of spatial dimensions we live in. 4 is the smallest number of colors sufficient to color all planar maps. The Buckminster Fuller Institute.