1. Irrational Numbers

2. InComMensurability Egyptiona and Babylonians calculated square roots
These were approximated
Not appreciated
Hippasus of Metapontum
Told the Pythagorean Secret
Died for revealing the discovery

3. InComMensurability Babylonians method of calculating square roots
Try to figure out which one works sometimes and which one is completely wrong.

4. InComMensurability First recorded proof that Euclid’s Elements
Here is the most popular proof

5. The History of pi
Definition of Pi
Ratio of

6. The History of pi
Definition of Pi
Ratio of

7. The History of pi Approximation of Pi
1650 BC: Rhind Papyrus x =
950 BC Temple of Solomon: π = 3

8. The History of pi Approximation of Pi 250 BC: Archimedes 3.1418
150 CE: Ptolemy used a 360 – gon
263 CE: Liu Hiu used a 192 regular inscribed polygon
480 CE: Zu Chongzhi used a gon

9. The History of pi Approximation of Pi
What do you have to plug into x to get this to equal pi/6?
Why can’t you just plug in the x that will give you pi?

10. The history of Will discuss more in length later
150 BCE: Euclid constructed
line divided into extreme and mean ratio by a point C
AB▪AC = AC▪CB
Not called golden ratio
Golden ratio is seen throughout history MANY times
Heron
Proclus
Abu Kamil
Al-Khwarizmi
Bernoulli
Fibonacci

11. The history of Relatively new 1610 CE: Napier wrote table of logs
1610 – 1670: e peaked around but not explicitly found
Area under hyperbola
Logarithmic curve
Series expansion of log(1+x)
1683 CE: Bernoulli compound interest limit

12. SOURCES History of Negative Numbers: http://nrich.maths.org/5961
MacTutor History of Mathematics: