Althea and the Mysteries of Triangles, Circles, and Pi

This is the second book in the series of Althea's Math Mysteries.  Althea and her friends - Sofia, Kiara, and Aiden - get together to explore geometry, pi, and trigonometry, with Mom's help.

Links mentioned in the book, in order by chapter.

If you'd like to form a math circle like the group of friends Althea worked with, do it! You could get a few friends together and play with these activities.

Activity Book

Activities:

• Geometry Challenges site  

  • (Aiden finds this for the pentagon. But why does it work?!)

  • Here's another construction site with lots more challenges (sadly, they must be done in order)

• Drawing and tearing. Proof that angles in a triangle add to 180.

• 5th postulate: https://mathenchant.wordpress.com/2018/11/17/between-the-world-and-the-mind/

• Alternate Geometries (find good sites)

  • Proof that square root of 2 is irrational (Here's a related article.)

  • History of Mathematicians Thinking About Euclid's 5th Postulate

• Measuring circles to define π

• Finding π’s value, with circles and triangles, and some proofs along the way

• Measuring angles. Making an inclinometer.

• Trigonometry

Extra Activities (not in the book):

• Making an angle of a given size,   and a harder (timed) activity

• Estimating the size of a given angle

History:

• Some Highlights

• Who Was Euclid?

• Euclid's Elements

Background:

• Why there's a bit more than 12 hours of daylight on the equinox.