Download presentation
Presentation is loading. Please wait.
Published byApril Burke Modified over 9 years ago
1
The proofs of the Early Greeks 2800 B.C. – 450 B.C.
2
Pythagorean Theorem Write an equation illustrating the relationship between the area of the rectangles, the area of the white smaller square, and the area of the large square Write an equation illustrating the relationship between the smaller squares, the rectangles and the larger square. Use transitivity and the subtraction property of equality.
3
Thales – 624 B.C. – 546 B.C. Started as a Merchant Well-traveled and curious Spent time in Egypt Why instead of How? First known Greek Philosopher Credited with first 5 theorems of Geometry
4
Mathematics of Thlaes Vertical angle Theorem Proof Angle a plus angle c make a straight line Angle c plus angle b make a straight line All straight lines are equal Angle a equals angle b Applications
5
Mathematics of Thlaes A circle is bisected by its diameter The bases of an isosceles triangle are equal Two triangles are congruent if the have two angles and one sides which are respectively equal
6
Mathematics of Thlaes An angle inscribed in a semicircle is a right angle. Thales is credited with the proof. Babylonia recognized this 1400 years earlier
7
A Greek Tragedy
8
The Sources of Greek Mathematics Euclid’s Elements in 300 B.C. Trumped all math before it No Primary Resources Eudemian Summary by Proclus around 500 A.D Had access to works lost to us Byzantine Greek Codics : 500 – 1500 yrs after Greek works Proclus Euclid
9
Pythagorus: 572 B.C. – 500 B.C Possible student of Thales Why do they think this? Founded Pythagorean School Mathematics Natural Sciences Philosophy Strange cultish rules Abstain from Beans Do not touch a white rooster Do not pick up what has fallen Not to stir the fire with iron Do not look in a mirror beside a light Do not eat meat
10
Arithmetica vs Logistic Arithmetica – Study of relationships between numbers Logistic – Computation Pythagoras started modern Number Theory Rafael: School of Athens
11
Divisors Definition: Examples:
12
Sum of Divisors Definition: Example: Compute s(284).
13
Perfect, Deficient and Abundant
14
Perfect, Deficient, or Abundant Exercise 1: Is 28 perfect, deficient or abundant? Exercise 2: Is 24 perfect, deficient or abundant? Exercise 3: Is 44 perfect, deficient, or abundant?
15
Euclid and Perfect Numbers Art of Problems Solving II
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.