1. The Middle Ages

2. The Middle Ages to Kepler There is a “down time” from 200 A.D. until 1200 A.D. The Library of Alexandria burns in 272 A.D. The Roman culture collapses into the Dark Ages.

3. The Catholic Church absorbs Aristotle’s science, which it teaches as doctrine.

4. Science Tool Kit in the 1200’s Roman numerals with no zero or place holder system (similar to Greeks). There was very little advancement in scientific tools and math since the Greeks.

5. The Romans had the same theories and misconceptions that the Greeks had, as after they conquered Greece they did not feel the need nor the urge to continue research.

6. Major contributors from 1200 to 1600 The Arabs (improved math) Nicolas Copernicus (sun- centered universe) Galileo Galilei (telescope, imperfect heavens, sun- centered universe)

7. Johannes Kepler (elliptical orbits and the related math)

8. Math from the Arabs Very slow transition from 1200’s to 1400’s. Our current Indian-Arabic numbering system (zero and place holder system) was imported. Algebra was also brought along.

9. Multiplication, however, was still performed with the doubling method.

10. Nicolas Copernicus (1473 – 1543) Copernicus had a wealthy family and a very good education Learned the (by now very cumbersome) Ptolemaic theory of the universe

11. Epicycles – circle within a circle Eccentrics – circle within a circle within a circle

12. The heliocentric (sun- centered) theory 1507 – Copernicus simplified the celestial calculations by assuming that the sun was the center of the universe. 1512 – He started working out the full mathematics of his new way of looking at the universe (this gave the theory validity).

13. To avoid the charge of heresy, he said that he was just “pretending” the sun was the center to simplify calculations.

14. Copernicus was not the first to suggest the sun was the center In 270 B.C., Aristarchus placed the sun at the center of the universe

15. This was not accepted because: We feel no movement on the earth There was no parallax (apparent shift in the position of nearby stars relative to distant stars).

16. If the earth is moving, an object thrown in the air should not fall straight down.

17. Galileo Galilei (1564-1642) Designed many experiments Swing time of pendulum always same Invented a gas thermometer Gravity experiments Made excellent telescopes

18. Observed mountains on moon, sunspots and the four moons of Jupiter

19. Galileo’s books “Starry Messenger” – his observations of the heavens “Dialogue on the Two Chief World Systems” (dim witted Simplicio represented the church’s earth centered view) Galileo was forced to recant his theory and his book was banned

20. Johannes Kepler (1571-1630)

21. As Imperial Mathematician Kepler had access to the best astronomical records of the time Kepler worked out the exact orbits of planets and found them to be elliptical

22. He developed the rigorous math to describe the various relationships related to elliptical orbits

23. Rene Descartes (day- kahrt) 1596 - 1650 Combined geometry with algebra Created the Cartesian coordinate system