Seeing with Two Eyes
For most people, seeing with two eyes is something we take for granted. Having two eyes helps us judge how close or how far away something is from us. Most sighted people have a dominant eye. You can test which one of your eyes is dominant by pointing at a distant object. If you close one eye, it will look as though you are pointing to that object. If you close the other eye, it looks like your finger is pointing at something completely different.
Seeing with two eyes gives you depth perception. Depth perception helps you understand how close or how far away something is from you. We can apply the concept of seeing with two eyes to how we see the world.
Questions:
- What happens when you bring your finger closer to your eyes?
- What happen if you open and close one eye at a time while you are touching your nose?
- How can you apply “Two-Eyed Seeing” to what you just observed?
The word geometry comes from the Greek words: geo (earth) and metron (measure).
Over 2,000 years ago, a man named Eratosthenes lived in ancient Greece. He wanted to know how big Earth was. He noticed the sun’s shadow was different in a different city than the one he lived in at a certain time of year. He knew how far the distance was between these two places. He knew when the sun was directly overhead because the shadows would be the shortest. He thought if he compared the shadows, he could figure out how big Earth was.
After measuring the shadows, Eratosthenes used his knowledge to determine the angle between the sun and the two locations. Then he used the angles he knew to find the angle between the two cities from the center of the earth. Once he had that angle, he could use the distance and the angle to determine the circumference of Earth.
His calculations were reasonably accurate compared to our current estimate of Earth’s size. He combined his knowledge of astronomy, geometry, and geography to developing a fairly accurate means to measure Earth
What the average person considers “geometry” is only one kind of geometry. Most people study geometry that is limited to 2-dimensions. Geometry is defined by a set of axioms and theorems. An axiom is a statement that is so obvious or well-established it is accepted as true. Axioms serve as a starting point for further investigation. A theorem is a statement that is proven true using previously established axioms. Axioms and theorems in one kind of geometry may or may not be valid in other types of geometry.
To measure an imperfect sphere like Earth, it is essential to understand geometry beyond 2-dimensions.
Activity: Discovering different kinds of geometry.
(Text to be adapted from Facilitator Guide)
Questions:
- What other kinds of geometry did you discover?
- Did you discover any kinds of geometry that works in three dimensions?