Transcript The Mysterious Circle
Lesson Objectives
1. You will develop an appreciation of circles.
2. You will explain the definition of a circle.
3. You will understand that a degree is equal to 1 /360. 4. You will explain why there are 360 degrees in a circle. 5. You will explain what a degree is and how many degrees there are in a circle.
The Mysterious Circle
Developed by Ivan Seneviratne
What is a circle?
A circle is a shape with all points in a plane at a fixed distance from the center. The given point is called the ‘CENTER’ of the circle. It is named by the center. The circle below is called circle A since the center is at point A.
A
Degrees in a Circle!
The 360-degree circle is 4400 years old. Have you ever wondered why there are 360 degrees in a circle? Seems rather weird doesn’t it.
You can blame the Babylonians this. They used the Sexagesimal system. it means that instead of using base 10 as we do they used base 60. Farmers probably counted the days in the year long before they cared about algebra. Combined with the fact that 360 is very close to the 365 days in a year, probably lead to the number being used in a lot of primitive seasonal calculations.
why 60? Well, 60 has a lot of advantages, especially before the day of calculators. The numbers 1-6 all divide nicely into it - therefore it’s easy to split a circle / hour / minute into fractions and get a whole number back.
Hipparchus of Rhodes
Hipparchus of Rhodes was born around 190 BC in Nicaea, Bithynia (now known as now Iznik, Turkey). He divided a circle into 360 degrees. He is the inventor of trigonometry and the Father of Astronomy. Although little else is known about him, it is probable that he died around 120 BC most likely in Rhodes, Greece.
Hipparchus (190 - 120 B.C.)
Mysteries Behind the Circles
Like many interesting shapes, circles are all around us every day. But how often do you notice them? Circles have fascinated people throughout the ages, so let's explore some of the most famous and mysterious circles in history.
The Story of Dido
A nice quality of the circle is shown in the story of Dido. This Phoenician princess escapes her town Tyrus (in today's Lebanon), after her brother (king Pygmalion) killed her husband. She went to the north coast of Africa, where she aimed to settle a new town.
Dido wanted to buy land from king Jarbas of Namibia, the emperor at that place.
So the emperor agreed that Dido could get as much land as the skin of an ox could cover.
Luckily, the princess was so clever to cut the skin in a long rope (probably more than a mile in length) and to lay this in the form of a circle, enclosing as much land as possible.
This meant the settlement of the city of Cartage (814 BC).
Stonehenge
Circle designs feature in the artifacts found from ancient civilizations and from more recent cultures all over the world. Prehistoric people built stone circles 4,000 years ago at Stonehenge in Wiltshire, England. Every June 21st, thousands of people flock to Stonehenge to watch a very special sunrise.
Crop Circles
One type of circle that still fascinates people today is the crop circle. Every year over 200 designs appear in crops around the world. In recent times they have been the subject of conspiracy theories, hoax and pranks, but there were reports of them in ancient times too. Nobody really knows how these complicated patterns are formed.
Squaring the Circle
There are many puzzles based on circles. One puzzle that the Greeks could never solve, and that no-one has ever solved since, is called 'Squaring the circle'.
Consider the problem of turning a circle into a square. Cut a circle out of a sheet of paper. Then cut the circle into pieces so that the pieces, when fitted back together, form a square having the same area as the original circle. You had to do it all by geometrical construction.
Perhaps first attempted by Anaxagoras (499 BC – 428) BC, it was finally proved to be mathematically impossible by Carl Louis Ferdinand von Lindemann (1852-1939) in 1882.
Olympic Symbol
Circles are still symbolically important. Today, they are often used to symbolize harmony and unity. For instance, take a look at the Olympic symbol. It has five interlocking rings of different colours, which represent the five major continents of the world united together in a spirit of healthy competition.
Archimedes
Archimedes, regarded as the greatest of Greek mathematicians, was born in 287 BC in Syracuse, Sicily, which was a Greek colony at the time. He was educated in Egypt by followers of the famous mathematician, Euclid. He wrote many works in mathematics centuries before its time. In a truly astonishing manuscript known as “The Method”, Archimedes discovered some of the key concepts of calculus.
He was killed in 212 BC by Roman soldiers while drawing circles in the sand - his last words being "Don't disturb my circles"! A true mathematician.
This presentation is developed by Ivan Seneviratne © 2007, purely for personal use.