81. Don Hatch's Home Page A $20 Holyhedron (fun geometry, no advanced math background required); A Canonical Reciprocation Center For Convex Objects (this was worth $1000! http://www.plunk.org/~hatch/

Don Hatch's Home Page Hi, welcome to my minimalist (so far) home page. NEW (Jun 22 2003): Manfred The Murderer I wrote this little song around Christmas 2002. Background: Manfred is a good friend of mine, who until recently had a very nice patch of kale in his garden. And he has bees. And the other day he chopped down a Christmas tree (or two). And his daughter Nicola hates fish. Lyrics Sheet music ( .pdf Synthesized piano recording, played as a round ( .ogg NEW (Jun 19 2003): Here are some research projects I've been working on lately. Both of these were posed as prize problems or bets by Professor John H. Conway of Princeton University. A $20 Holyhedron (fun geometry, no advanced math background required) A Canonical Reciprocation Center For Convex Objects (this was worth $1000! some advanced math required) Here are some pretty pictures of hyperbolic tesselations Java version (in progress). Some more java applets, without much explanation... Magic Cube 4D Polygon Reciprocation (Dual) Demo Modern Portfolio Theory (Mean Variance Analysis) Hyperbolic Splining Demo ... Tyler (with Melinda Green) Some artwork based on fractal zooming: A movie...

82. Terrific Tessellations Plan. Title Terrific Tessellations. Subject(s) Math transformational geometry, tessellations, symmetry, patterns. Intended Grade Level(s) 4 6. http://www.remc11.k12.mi.us/bstpract/bstpract/144/144.htm

Elementary Lesson Plans Middle School Lesson Plans High School Lesson Plans Lesson Plans by Teacher Name ... Main Page MAISA and the REMC Association of Michigan Best Practices in Technology Integration Plan Title: Terrific Tessellations Subject(s): Math: transformational geometry, tessellations, symmetry, patterns. Intended Grade Level(s): 4 - 6 Download PDF version Description: Tessellation: A tiling, made up of the repeated use of a shape that completely fills a plane without gaps or overlaps.Terrific Tessellations Curriculum Benchmarks: MI.MAT.I.1.E.1 Recognize, describe, and extend numerical and geometric patterns. MI.MAT.I.1.E.4 Explore various types of numeric and geometric patterns (repeating, growing, shrinking). MI.MAT.II.1.E.2 Describe the attributes of familiar shapes. MI.MAT.II.1.E.4 Draw and build familiar shapes. MI.MAT.II.1.E.5 Explore ways to combine, dissect, and transform shapes. MI.MAT.II.1..E.6 Recognize parallel and perpendicular line segments and figures that have similarity and/or congruence. MI.MAT.II.2.E.2 Locate and describe objects in terms of their orientation, direction and relative position, including up, down, front, back, N- S- E- W,flipped, turned, translated; recognize symmetrical objects and identify their lines of symmetry.

83. Search Results An = (648.20052) tessalations; colouring; Dirichlet http://www.emis.de/cgi-bin/zmen/ZMATH/en/zmath.html?an=648.20052&format=complete

84. Investigating Patterns: Symmetry And Tessellations TOP. ACTIVITY 11 (Paper Scissors Pentagon) Title Some Golden geometry. Comment Well, try this! Title Triangle geometry Triangles. Comment http://www.camosun.bc.ca/~jbritton/jbsymteslk.htm

Investigating Patterns Symmetry and Tessellations ACTIVITY LINKS ACTIVITY 1 (What is Mathematics?) Title: What is Mathematics? Comment: Observations on the the nature of mathematics from Pathways to School Improvement . Includes: "Mathematics should include experiences that help students to shift their thinking about mathematics and define mathematics as a study of patterns and relationships." Title: Pythagoras: Music and Space Comment: A brief introduction to Pythagoras' observations on the relationship between music and number. Graphics show music intervals expressed as mathematical ratios. If you have a plug-in that can play sound, you can pluck the strings to hear the notes. Title: How to Make Ukrainian Easter Eggs Comment: Tells you everything you need to know about the basics of making pysanky (Ukrainian Easter Eggs). Click on any design and you'll be taken to the instructions for it. Challenge students to explain why the egg at the right from Pysanky Designs (Advanced Designs) is different from the others. [Click on the egg for the solution.]

85. Tantalizing Tessellations!! 45 resources). The geometry Center brief overview of TesselMania CD Rom program. What is a Tessellation answers what is a tessellation. http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html

Integration This unit integrates math with subjects such as language arts and arts education. Throughout our activities we have asked the students to respond to the concepts of tessellations. They will write definitions and assess how well their groups worked together. In addition, we have exposed the students to tessellations in the environment, including interior design. If one can locate some prints by M.C. Escher, students will see how their topic can become a famous art form. As a culminating activity, students will create a classroom quilt. The quilt will be a combination of a geometric shape (the square piece of paper) and a geometric transformation (translation, rotation, or reflection). This mathematical topic can also be explored in other subjects. Quilts, and the importance of quilts, can be studied through social studies. The classroom quilt can be considered symbolic for the class; each student could compose a story to explain her/his quilt patch. In science, when students are studying insects, for example, they can connect tessellations to the wings of a fly or butterfly. These are some of the ways we think our topic of tessellations can be integrated across the curriculum. CELs Communication - students will communicate their understanding of the different tessellation concepts in written form. Since a number of lessons involve the teacher modelling a technique, students will have an opportunity to develop their listening skills. Because there is a lot of direct teaching involved, it will require the teacher to use clear and precise language. Students will also be encouraged to use "math language" - rotation, slide, trapezoid, hexagon, etc.

86. Tessellation Tutorials Tessellation Tutorials A series of tutorials that teach students how to tessellate (somewhat in the style of the art of M.C. Escher) using HyperCard for black and white and/or HyperStudio for http://rdre1.inktomi.com/click?u=http://mathforum.org/sum95/suzanne/tess.intro.h

87. Math Forum: What Is A Tessellation? An illustrated explanation of what a tessellation is in mathematical terms. http://mathforum.com/sum95/suzanne/whattess.html

What Is a Tessellation? About This Project What is a Tessellation? Tessellation Tutorials Tessellation Links For information on tiling see: What is a Tiling? View the MidPoW (March 11 - 25, 2002): Tiling Triangles Definition A dictionary will tell you that the word "tessellate" means to form or arrange small squares in a checkered or mosaic pattern. The word "tessellate" is derived from the Ionic version of the Greek word "tesseres," which in English means "four." The first tilings were made from square tiles. A regular polygon has 3 or 4 or 5 or more sides and angles, all equal. A regular tessellation means a tessellation made up of congruent regular polygons. [Remember: Regular means that the sides of the polygon are all the same length. Congruent means that the polygons that you put together are all the same size and shape.] Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons.We can't show the entire plane, but imagine that these are pieces taken from planes that have been tiled. Here are examples of a tessellation of triangles a tessellation of squares a tessellation of hexagons When you look at these three samples you can easily notice that the squares are lined up with each other while the triangles and hexagons are not. Also, if you look at 6 triangles at a time, they form a hexagon, so the tiling of triangles and the tiling of hexagons are similar and they cannot be formed by directly lining shapes up under each other - a slide (or a glide!) is involved.

88. Kenston School District ~ Chagrin Falls, Ohio ~ USA K E N S T O N. S C H O O L S. School Closing Alert. Early Learning Center. Kenston Community Education. Board of Education. Gardiner Elementary. Computer Technology. School Calendars. Timmons Elementary. Kenston Foundation. Alumni Page http://www.kenstonlocal.com/khs/math/top4.html

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