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Pythagorean Treasury

Shape and Space Powerpoint Presentation

Pythagorean Treasury

This is a PowerPoint math or maths presentation on The Theorem of Pythagoras.
We start by looking at some of characters included in Raphael's fresco "The School of Athens" from the Vatican Museum. We see Plato and Aristotle as the central characters and then show others including Socrates, Euclid and Pythagoras. The presentation then continues as follows:
Slides 4 and 5: Students are given the chance to discover the Theorem of Pythagoras for themselves using the worksheets provided. This shows triangles for the first 3 Pythagorean triples/triads set on the background of a square grid. The students are asked to draw the squares on each of the sides and record the results in the table provided. When the teacher is ready the squares will appear and the board and the table will be completed. Hopefully someone will figure it out and the Theorem is then made explicit.
Slides 6: States the general Theorem of Pythagoras
Slides 7 to 9: The first 3 triples/triads are looked at again and elaborated by the teacher.
Slides 10 and 11: Perigal's dissection is demonstrated and the students have a worksheet so that they can participate in it.
Slides 12 to 22: Basic Pythagoras questions + applications including (diagonal of a rectangle/kite, leaning ladder, boat and aircraft journeys plus vectors.
Slides 23 to 29: Historical and cultural aspects of the Theorem including a look at its use in Ancient Egypt, Mesopotamia (includes the Plimpton 322 tablet) and finally ancient Greece. We take a brief look at the Pythagorean Brotherhood and their philosophy as well as their work on understanding the mathematical principals behind music. We also look at the discovery if incommensurable magnitudes in particular the discovery of the irrationality of root 2. The Pythagorean Pentagram and its meaning as well their use of figurate numbers are also investigated.
Slide 30: Gives a menu of the 7 proofs of Pythagoras' Theorem that are demonstrated. These are:
1. Possibly Greek (Pythagoras)/Chinese proof of the theorem
2. Bahskara’s proof of Pythagoras' Theorem
3. President Garfield's Proof of Pythagoras' Theorem
4. John Wallis's Proof of Pythagoras' Theorem
5. Euclid's (Windmill Proof) of Pythagoras' Theorem (Elements (1.47)
6. Euclid's Converse of Pythagoras' Theorem (Elements (1.48)
7. Perigal's visual demonstration (included for completion).
Sldes 31 to 33: Some famous people (Hobbes, Lincoln and Einstein) and the impact of deductive proof.
Slides 34 to 41: The 7 Proofs
Slides 42/43: We look at the use of Pythagoras's Theorem in 3D problems.
Slide 44 to 46: Irrational lengths and growing spirals.
Slides 47/48: Determining the general rule for certain sets of Pythagorean Triples.
Slides 49/50: Investigate other similar shapes (apart from squares) drawn on the 3 sides of right-angled triangles.
Not everything has been mentioned and there's quite a lot more. This is an excellent resource on Pythagoras and his Theorem with lots of background information.

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