Symmetry and Tessellations

• Transformations and Tessellations-- Symmetry [Elkins, 7/2/1995]
  We must teach about reflectional symmetry, line s., axis of s., line of s., mirror s., vertical s., horizontal s., horizontal and vertical s., toysyionsl d., and point s.

• Where's the Math in Tessellations? [Barass, 1/20/1996]
  My son is doing an honors project for his 9th grade algebra class. He is supposed to make the connection between math and art. The only information we come up with is about M.C. Escher and some examples of tessellations.

• Tessellation Proof [Catherine, 6/11/1996]
  I am looking for the proof of the statement that only three regular polygons tessellate in the Euclidean plane.

• History of Tessellations [Caveman, 12/10/1996]
  A students asks questions about the history of tessellations.

• Tessellations and Symmetries [Fang, 06/07/1997]
  How do you make a tessellation with a rotation, reflection, and translation all in one shape?

• Rotational Symmetry [Auge, 11/05/1997]
  I am looking for a precise definition of rotational symmetry of a figure in a two-dimensional plane.

• Center of Mass [Genevieve, 02/22/1999]
  Find the center of mass of a thin plate of constant density covering the region bounded by the parabolas y = 2x^2-4x and y = 2x-x^2.

• Math in Card Games [Joshi-Powell, 10/06/2000]
  How is math involved in creating and playing card games?

• Numbering the Faces of Dice [Cotterill, 02/27/2001]
  How many ways are there to make dice out of the Platonic solids (i.e. 4, 6, 8, 12, and 20 sides)? How many of those ways have opposite face sums equal? What would the opposing face sums be for each type?

• Symmetry Proof [Jane, 09/27/2001]
  Given an angle with vertex O and a point P inside the angle, drop perpendiculars PA, PB to the two sides of the angle, draw AB, and drop perpendiculars OC, PD to line AB. Then show that AC=BD.

• Horizontal and Vertical Symmetry [Lizzy, 10/27/2001]
  I have to find an example of horizontal symmetry, and I have no idea what that is.

• 2^4 = 16 AND 4^2 = 16 [Yvonne, 10/29/2001]
  Can you think of any other pair of unequal numbers that share the same relation as 2 and 4 in the above example? What was your strategy?

• Etymology of the Word Tessellation [Cindy, 11/05/2001]
  Are tessellations related to the tesseract in Madeleine L'Engle's _Wrinkle in Time_ series?

• Inversions [David, 01/09/2002]
  Is there a name for words such as SWIMS that look the same after a rotation of 180 degrees (flipped and upside-down to my grade 3 students)?

• Colour Combinations on a Cube [Daniel, 02/08/2002]
  If each side of a cube is painted red or yellow or blue, how many distinct colour patterns are possible?