ACE 3.2 More rep-tiles

Today we studied problem 3.2 on pages 40-41 of the handout (which can be downloaded here), and worked with triangles to find out if they were rep-tiles. We found out that indeed triangles can tile to create similar triangles, either by putting smaller triangles together or subdividing triangles into similar smaller triangles.

The perimeter increases with the scale factor, so if the scale factor is 1.6, the perimeter will be 1.6x the original. And if the scale factor is 0.5, the perimeter will be 0.5 of the original.

We also found out that the area of a new similar figure is equal to the square of the scale factor times the area of the original figure. So if the scale factor is 1.6, and the area of the original figure is 3 square units, then the new image will have an area equal to 1.6 x 1.6 x 3 square units. And if the scale factor is 0.5, the new image will have an area equal to 0.5 x 0.5 x 3 square units.

Class notes can be downloaded here.

For homework, please choose one of the options below on the handout, which can be downloaded here.

Option 1
Problems 4-6 and 26-27

Option 2
Problems 4-5, 26-27, 34, and 37 (an interesting example of a fractal)

Due Monday, November 30. Do the homework tonight to have a math-homework free vacation. And don't forget the POW is also due Monday, November 30.

Have a great break!