Number Devil Activities: The Tenth Night

On the tenth night of The Number Devil, Robert finds himself freezing in a snowy scene and exploring the golden ratio.

The Snowflake Formula:

Did you know there is a mathematical formula to make a snowflake?  A Swedish mathematician, Helge von Koch depicted a mathematical curve that creates a fractal made from equilateral triangles.  Check out this animation of the "snowflake" formula in action.  Make your own snowflake fractal.  Print and cut out these triangles.  In the center of a blue piece of paper, glue one of the two largest triangles.  Next glue the other large triangle upside down to make a Star of David shape.  On each of the 6 points glue the 6 medium triangles to make 6 more Stars of David.  Repeat for the 18 small triangles.

Bonus: Can you make 54 smaller triangles to glue on the tips of the last 18 Stars of David?

Bonus 2: Learn more about Helge von Koch. Create a notebook page for him.  At the top of the page you might give him a nickname that will help you remember who he is such as Snowflake Designer.

Define:

What is an unreasonable number?  Look at the "Seek and Ye Shall Find List" in the back of the Number Devil for the official term and review what it is.

Discovery of the Golden Ratio:

The Number Devil introduces Robert to the most beautiful number known to man.  Didn't know numbers could be beautiful?  Well, the number is 1.618... I bet you're rolling your eyes with Robert wondering how an irrational number such as 1.618 can be beautiful.  1.618 is called the golden ratio and it is found through out the human body, nature, art, and architecture.   Practice your own calculations to find the golden ratio in any two numbers just like the Number Devil with this simple to follow worksheet.  Next, learn more about the golden ratio.  This website has an easy to understand definition and great activities.

The Invention of a Quang:

What is a quang?  Who knows?  It's from the Number Devil's own imagination.  Invent your own measurement.  Using a strip of cardstock or posterboard make markings equally along the edge to show how long your measurement is.  What are you going to call it?  How does it compare to a standard measurement such as an inch or  a millimeter (ie. Is it about 2 1/2 inches or 22 millimeters)?

Testing D + S - L = 1:

Choose an item to represent a line and a dot.  It could be red vines and life savers or pretzel rods and banana chips or Tinkertoys sticks and wheels.  Create your own figures with a dot at both ends of every line, as demonstrated by the Number Devil on page 203.  Record your findings on this lab sheet.

Build Your Own Polyhedron:

The Number Devil gives several polyhedron examples on pages 204-210.  Use these patterns to build your own. What is the name of your polyhedron?

Bonus:  In this lesson we've made polygons and polyhedrons.  Define each.  What is the difference?

Bonus 2:  Do you crochet?  Try crochetting this dodecahedron.

Review:

Who is Bonacci?  Look back at your notebook page if you need help remembering.