Technology Integration Presentation

Thales' PowerPoint

http://www.screencast.com/t/U6h2ePqsA0aX

Lesson Plan

Ancient Roots of Math: Thales, the Egyptians and Measurement

Lecture

 Joy of Mathematics: Thales and the Great Pyramids

(Use to inspire exploration)

Born: Approximately 624 BC, Miletus, Asia Minor. (Now Balat, Turkey)

Died:   Approximately 547 BC

Thales was an engineer by trade; Thales went to Babylonia and Egypt to study with the priests, where he learned of mathematical innovations and brought this knowledge back to Greece. Thales also did geometrical research and, using triangles, applied his understanding of geometry to calculate the distance from shore of ships at sea.

Thales was the first Greek scientist that we know of who did not try to explain the weather and the stars and planets as things controlled by the gods. Instead, Thales thought there were scientific explanations for these kinds of things. That doesn't mean Thales got everything right! He thought that water was the basis of all living things. Thales thought everything living was basically made out of water. Thales was right that everything is made out of the same things, but those things are electrons and protons, not water. But some things Thales did get right. He understood that the earth was round, and that the moon was lit by light reflecting from the sun.

Thales was also an important mathematician. He figured out a way to measure the height of one of the Egyptian pyramids. He waited until a time of day when his own shadow was the same height that he was, and then he measured the shadow of the pyramid. (You can try this for yourself - does it work?)

And he was able to prove several interesting mathematical ideas. Thales proved that a circle is bisected by its diameter, the angles at the bases of any isosceles triangle are equal if two straight lines cut one another, the opposite angles are equal if two triangles have two angles and a side in common, and the triangles are identical.

Google Earth on iPad – Locate Thales birthplace; Balat Turkey – following his path from his birthplace to Babylonia and then to Egypt, What were some things you observed about his travels?

Student’s will use their iPad and search the internet to answer this question: What major event do ancient writings say that Thales predicted in 585 B.C.?

Answer: It is also reported that Thales predicted an eclipse of the Sun in 585 BC. The cycle of about 19 years for eclipses of the Moon was well known at this time but the cycle for eclipses of the Sun was harder to spot since eclipses were visible at different places on Earth. Thales's prediction of the 585 BC eclipse was probably a guess based on the knowledge that an eclipse around that time was possible.

PowerPoint Presentation

Journal Assignment

What is a “Sage”?

Answer: The Seven Sages (of Greece) was the title given by ancient Greek tradition to seven early-6th-century BC philosophers, statesmen and law-givers who were renowned in the following centuries for their wisdom. Traditionally, each of the seven sages represents an aspect of worldly wisdom. Thales is the first well-known philosopher and mathematician. His advice, "Know thyself,"

Discussion: Thales was considered a philosopher, mathematician and a scientist. Today we think of people who become masters at philosophy, mathematics or science to be very different people. How do you think one person could be all of these?

Thales’ story is an example of mathematical ideas being exchanged through one person’s travels. He probably learned geometry from the Egyptians and astronomical science from the Babylonians, and took his knowledge back to his native Asia Minor.

Why were the Egyptians such good geometers (literally, “earth measurers”)

In ancient times, people measured things with the measuring stick they took with them everywhere – their hands, arms, fingers, and feet of course!

A cubit is the length of a forearm, from the elbow to the fingertips.

A palm is the width of your four fingers excluding the thumb.

A finger is the width of, well, a finger.

In Egypt, a royal cubit was equal to the length of seven of Pharaoh’s palms.

Activities

Try measuring your own personal cubit, and your own palm this way. If you measure it with a piece of string and cut the string the length of your cubit and palm, you can then compare the length of the palm to the cubit. How many times can you stretch the palm along the cubit, is it close to seven times?

Now, compare your measurements with your classmate sitting closest to you. Are they the same? If your cubits are different, what about the ratio (number of times you can stretch the palm along the cubit length) of the palm to the cubit – is it the same?

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Math Ideas associated with Thales:

·         Measurement

·         Geometry of triangles

·         Problem Solving

·         Egyptian Multiplication

·         Area, perimeter

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Vocabulary related to this lesson:

·         Triangle

·         Angle

·         Pyramid

·         Mathematician

·         Eclipse