Math + Art = Marth

Math is full of art and art is full of math. Here are some lessons at Village Elementary School with Kate, and Natalie - both sixth grade students. The class taught by Miss Suki.

Tessellations are patterns of geometric design. It is a pattern made up of one or more shapes, completely covering a surface without any gaps or overlaps. The shapes must fill the space all around a common vertex point.

Four squares fit around one point.

The pattern can continue in the plane indefinitely.

Do triangles tessellate?

Kate and Natalie are exploring what shapes will tessellate. They are asked to build a hexagon with congruent equilateral triangles (the green triangle with Pattern Blocks).

The next question, "Can right triangles also be made into a hexagon?

Some creative solutions:

Natalie ....................................................Kate........................................................................

To tessellate the six right triangles must be around a point like the hexagon built with equilateral triangles.

The next challenge is to build a hexagon with six congruent right triangles that will fit around a point.

Which solution is correct?

The bottom figure is correct.

Do other shapes besides triangles tessellate?

Regular four sided figures are tried. We already know that squares tessellate.

Will the blue pattern block tessellate?

 Kate's blue pattern block (four sided regular rhombus) design does tessellate.

Here's another exploration. Will two or three shapes together tessellate?

Rainbow Pattern Blocks are used to create these designs below.

Natalie

KateNatalie