Inspiration from Bronowski's Ascent of Man

The best ever Christmas present: the full set of Jacob Bronowksi's staggering 1973 BBC series "The Ascent of Man" - a triumphant presentation of science, mathematics and art, delivered with warmth and style by an amazing human being. Unlike some other contemporary BBC series, this series remains fresh and exciting. The only slightly jarring element is the repeated use of "man" rather than "people" - but that's an artifact of the age. 

Jacob Bronwski on the island of Samos, exploring right triangles.

In Episode 5, "The Music of the Spheres", Bronowski reveals the mathematical elephant in its full glory. There is enough material in this one episode to last a full high school mathematics curriculum. I'm hoping my students this year will take some pleasure in watching some of extracts of this episode - we shall see! At the end of this post is a breakdown of the content. If you don't own the DVD, many extracts are available on YouTube.  Here is a wonderful segment on Pythagoras which could easily be extended into a student activity - either using physical media, or with software.

Topics Bronowski covers in Episode 5
with duration and suggested school grade level (using NSW syllabus)

Chapter 1: Pythagoras discovers mathematical relationships of notes of vibrating strings  (7 mins - maths starts at 4 min mark; Year 7/8)
Chapter 2: The nature of right triangles - reflection, rotation and Pythagoras' Theorem (7 mins; Year 8)
Chapter 3: Ptolemy - astronomy and geometry (4 mins; Year 8)
Chapter 4: Rise of Islam and flourishing of mathematics in the middle east (6 mins; Year 8)
Chapter 5: Tesselations at the Alhambra - good exposition of rotations and symmetry (8 mins; Year 7/8)
Chapter 6: Crystals forms - geometric structures in nature - related to symmetry (3 mins; Year 7/8/9)
Chapter 7: East meets West at Toledo: Arabic mathematics and astronomy arrives in Europe (6 mins)
Chapter 8: Geometric perspective (some nudity),  the dimension of time, Kepler orbits, calculus mentioned (8 mins; Year 10)

There is a significant amount of positive coverage of Middle Eastern culture in this episode, which should resonate with some student demographics who might otherwise feel mathematics is always about the Western World.