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---------------------------- 2353 - What Creativity from the Ancient Greeks?
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- Archimedes of Syracuse born in 287 B.C. and died 212 B.C. During his life he traveled to Egypt and the city of Alexandria. While he was there he invented the hydraulic screw to lift water out of the rivers and dump it into irrigation canals.
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- He mathematically documented the power of the block and tackle and the lever. He made the famous quote about the lever, “ Give me a place to stand and I will move the Earth”
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- In 214 B.C. the Greeks were at war with the Romans. Archimedes helped the Greek Army by designing catapults as machines of war. Archimedes proposed arming the Greek soldiers with mirrors and as the Roman ships sailed into the harbor of Syracuse focus the sunlight on the ships and set them ablaze.
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- In 212 B.C. the Romans conquered Syracuse and he was killed by a Roman soldier. He was 75 years old and at the time was working on another math problem at his desk.
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- Archimedes first calculated the volume of a sphere to be 4/3rds times Pi times the cube of the radius. He came up with this by first nesting a sphere inside a cylinder where the diameter of the sphere equaled the height of the cylinder. The volume of the cylinder could be calculated as the area of the circle, Pi*r^2. at on end times the height of the cylinder, 2*r, or 2*Pi* r^3 for the volume of the cylinder.
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- Archimedes’ genius was in using the concepts of calculus to determine that the sphere was 2/3rds the volume of the cylinder. He broke the volume down into thin slices and then “integrated”, or summed, all the slices to get the whole.
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------------------------------- Volume of a sphere = 4/3*Pi*r^3.
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- Archimedes discovered the value of Pi by using the same method of calculus. He fitted a hexagon inside a circle and measured the perimeter by adding up the lengths of 6 sides of 6 equilateral triangles. Each side being the radius of the circle. The circumference of the circle must be a little more than 6 times the radius.
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- He recognized that all circles have a circumference that was directly proportional to the length of the diameter. To find the equality he had to discover the constant of proportionality, that we call “Pi“.
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- To make the hexagons inside the circle closer and closer to the perimeter he divided again to get a 12 sided polygon, then a 24 sided polygon, then a 48 sided polygon, then a 96 sided polygon. Each time the polygon perimeter approaching the shape of a perfect circle. He calculated Pi to be 3.14 times the diameter of the circle.
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- When Archimedes was 47 years old another Greek, named Eratosthenes calculated the circumference of the Earth. Syene was a city in southern Egypt and on June 21st, the Summer Solstice, the Sun was directly overhead as evidenced by the Sun’s reflection at the bottom of a deep well. Alexandria was a city at the north coast of Egypt.
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- At the same time of year, also at high noon, the Sun cast a shadow at 7.2 degrees from the vertical. The distance between Alexandria and Syene was 5,000 stadia. The “stadion” was equivalent to 157.5 meters.
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- Eratosthenes figured that the Sun’s rays were parallel lines. The angle at the center of the Earth drawn to intercept Alexandria and Syene on the surface was also 7.2 degrees. The ratio of the angle 7.2 degrees to the circumference of Earth , 360 degrees, must be the same as the 5,000 stadia to the circumference in stadia.
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-------------- 7.2 / 360 = 5,000 / circumference
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-------------- circumference = 250,000 stadia.
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- Today’s measure of stadia at 157.2 meters times 250,000 stadia = 39,300,000 meters.
- Today’s measure of the circumference of the Earth is 24,900miles. At 1,610 meters per mile that equals 40,089,000 meters.
- Eratosthenes got to within 2% of the correct answer in his calculation 240 years before the birth of Christ. How cool is that?
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- Socrates was a great teacher, his student was Plato (B:428 B.C.), his student was Aristotle (384-322 B.C.) and his student was Alexander the Great.
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- Aristotle, the teacher, founded his school in Athens, Greece, in 335 B.C. when he was 29 years old. His father died when he was 10 years old. He lost his mother too and was raised by a family friend until he was 17. Then he entered the academy founded by Plato and was there as a student / teacher for 20 years.
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- Aristotle was known to have a mind of his own. He never felt bound by his teacher’s teachings. “It is the mark of an educated mind to be able to entertain a thought without accepting it.” (It is a mark of an educated teacher to teach students to think for themselves).
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- Aristotle believed that reality was what you could observe and touch. He had a scientific mind. The topics in his school included physics, astronomy, zoology, and psychology. And, these fields of study did not exist before he originated them.
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- Aristotle used inductive reasoning. He started by developing underlying principles derived from observations. He insisted on defining each of his subjects, first for similarities, then for differences.
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- He used logic to determine axioms and then axioms to derive theorems. He would establish facts by taking two known quantities to establish a third. Fact: To be a teacher you must have a student. Fact: To be a student you must want to learn. Therefore, teachers can only teach people you want to learn.
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- These were ancient times. Aristotle had to make his observations fixing time without a clock, comparing degrees of heat without a thermometer, observing the heavens without a telescope, and observing the weather without a barometer.
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- Aristotle was a teacher who listened eagerly to others; he freely altered his views when presented with compelling evidence that he was wrong. He often went back and modified his own writings when he learned more.
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- His school was called the Peripatetic School because he held his lectures and discussions while walking around in the school gardens. (peripatetic means “walk about”).
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- Modern teachers would do better teaching if they had their students stand and/or walk and not simply sit at a desk. Socrates taught by always answering a question with a question. He believed that active participation required that the student figure out the answers for themselves.
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- Aristotle’s writings became a “ university library”, over 150 volumes, and eventually they served as the kernel for the great Library of Alexandria.
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- Every teacher must have a student. Every student must want to learn. Confucius say: “First you must become a student then a teacher will come.”
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- Great teachers beget great teachers. You have not really mastered a subject until you teach it to someone else.
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- These old guys were pretty smart.
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- See also Review #651 - Plato’s Dialogue for Justice
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- May 5, 2019. 667 1125
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--------------------- Sunday, May 5, 2019 -------------------------
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