Have you ever played with shapes and patterns? That's what geometry is all about! It's the study of lines, angles, shapes, and space. From drawing cool designs to building structures, geometry is an important part of our world.

I wanted to demonstrate how parallax works in measuring distances on a small scale, and to see if one method was more accurate than the other. My hypothesis was that the tangent method would be more accurate than the radian method.

Can you measure the distance to an object using only angles and a baseline? Parallax is a technique that calculates how far away something is by viewing it from two different positions. Astronomers use it for distant stars. You can test it across a room.

You set up a target about 20 feet from a wall. You mark two viewing points on the wall and measure the angle between them with a protractor and string. Then you calculate the distance using two different methods: the tangent method and the radian method.

Both methods give accurate results at this scale. Neither one proves clearly better than the other for short distances.

Project Title: Parallax

Objectives/Goals

I wanted to demonstrate how parallax works in measuring distances on a small
scale, and to see if one
method was more accurate than the other. My hypothesis was that the tangent
method would be more
accurate than the radian method.

Methods/Materials

I used a large room with a blackboard at one end. About 20 feet from the wall, I
placed a "target," a
yardstick taped to a chair so that the top of the yardstick was about five feet
off the ground. I then marked
on the board, the two points at which the target was viewed from two points
equidistant from a midpoint
on the baseline. In some cases the two viewpoints were two eyes on a person's
face.
I then used a protractor, placed on the target, and a string to measure the
degrees those two points on the
wall were apart. Using that measure, I then used two methods to measure the
distance from the the
baseline to the target.
The tangent method is using the right triangle formed by one viewpoint, part of
the baseline, and the
distance to the target. Knowing the angle of the viewpoints on the board, allows
you to find out all three
angles in the triangle. You also know the measure on the baseline from the
midpoint to one viewpoint.
You can then look up the tangent and find out the distance to the object.
To use the radian method, you have to imagine a circle that the target is the
center of. The angle of the
two points on the board gives you the measure of the arc between the two
viewpoints on the baseline.
Putting the length of the distance between the viewpoints (the radian) over the
arc it cut off in the circle,
you can find out the circumference of the circle. You then divide by 2pi to
determine the radius, which is
the distance to the object.

Results

I found out that using parallax on this small scale was an accurate way to
measure distances. However,
there was no significant difference in the accuracy of the two methods
Conclusions/Discussion
Parallax works but it requires very accurate measurements of the angles
involved. On this small scale,
there was not a significant difference between the two methods. On a large
scale, my hypothesis might be
correct because the difference between the radian and the length of the arc
would increase.

Summary Statement

I wanted to demonstrate how parallax works and show which method was more
accurate.


Parallax: Tangent vs. Radian Methods

Demonstrate how parallax works in measuring distances on a small scale

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Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

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Parallax: Tangent vs. Radian Methods

Hypothesis

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