Twenty-four lectures (30 min. ea.) explaining mathematical thinking.

Accompanying guides include biographical information, lecture notes and outlines, timelines, glossaries, and bibliographical references. In two containers.

disc 1. lecture 1. Great ideas that bring our world into focus -- lecture 2. How many? Counting surprises -- lecture 3. Fermat's last theorem and the allure of numbers -- lecture 4. Pining for nature's numbers -- lecture 5. Sizing up the Fibonacci numbers -- lecture 6. The sexiest rectangle disc 2. lecture 7. The hidden beauty of the golden rectangle -- lecture 8. The Pythagorean theorem and geometry of ellipses -- lecture 9. Not-so-Platonic relationships in Platonic solids -- lecture 10. Hunting for a sixth Platonic solid -- lecture 11. Is there a fourth dimension? Can we see it? -- lecture 12. The invisible art of the fourth dimension disc 3. lecture 13. A twisted idea--the Möbius band -- lecture 14. A one-sided, sealed surface--the Klein bottle -- lecture 15. Ordinary origami--creating beautiful patterns -- lecture 16. Unfolding paper to reveal a fiery fractal -- lecture 17. Fractals--infinitely complex creations -- lecture 18. Fractal frauds of nature disc 4. lecture 19. Chance surprises--measuring uncertainty -- lecture 20. Door number two or door number three? -- lecture 21. Great expectations--weighing the uncertain future -- lecture 22. Random thoughts--randomness in our world -- lecture 23. How surprising are surprising coincidences? -- lecture 24. Life lessons learned from mathematical thinking.