Submitted by Editor
Project Assignment Think of a question that asks about a cause and effect relationship between two measurable quantities. (eg.. does fingernail length affect typing speed?)
1. Write two different "how does _____ affect _____" questions. 2. Select the question that makes the most sense to you and explain why you have chosen it. 3. Write a hypothesis to answer your question. 4. Graph your data using appropriate choices of scales and axis. 5. In pencil, draw your "best" line. 6. Find the equation of your line.
Respond to the following questions 7. What do the variables in your equation represent? What does the equation represent? 8. Was your data positively correlated, negatively correlated or neither? Give possible explanations for the relationships or absence of relationships that you see in the data. 9. Use your equation to predict two data points not represented by the data. How good do you think these estimates are? why? 10. What information does the slope indicate?
Present your findings in a 3-4 pages handwritten report. Graph must be included.
You can use rods of integer sizes to build "trains" that all share a common length. A "train of length 5" is a row of rods whose combined length is 5. Here are some examples:
Area of an Arbelos
Objective: Prove that the area of the arbelos (white shaded region) is equal to the area of circle CD.
What is an arbelos? The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AB, and each semicircle is tangent to the other two. The arbelos has been studied by mathematicians since ancient times, and was named, apparently, for its resemblance to the shape of a round knife (called an arbelos) used by leather workers in ancient times.
An interesting property of the arbelos is that its area is equal to the area of the circle with diameter CD. CD is along the line tangent to semicircles AC and BC (CD is thus perpendicular to AB). C is the point of tangency, and D is the point of intersection with semicircle AB. Can you prove that the area of circle CD equals the area of the arbelos?
To do this project, you should do research that enables you to use the following terms and concepts:
Materials and Equipment
Objective : The objective of this project is to prove whether or not the birthday paradox holds true by looking at random groups of 23 or more people.
Introduction: The Birthday Paradox states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true?
Experimental Procedure 1) First you will need to collect birth dates for random groups of 23 or more people. Ideally you would like to get 10-12 groups of 23 or more people so you have enough different groups to compare. Here are a couple of ways that you can find a number of randomly grouped people.
2) Next you will need to sort through all the birth dates you have collected and see if the Birthday Paradox holds true for the random groups of people you collected. How many of your groups have two or more people with the same birthday? Based on the birthday paradox, how many groups would you expect to find that have two people with the same birthday?
3) Tabulate/Organize your data and findings in a 3-4 pages handwritten report
Objective: The objective of this project is to prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.
Introduction : The figure below shows a semicircle (AE) with a series of smaller semicircles (AB, BC, CD, DE,) constructed inside it. As you can see, the sum of the diameters of the four smaller semicircles is equal to the diameter of the large semicircle. The area of the larger semicircle is clearly greater than the sum of the four smaller semicircles. What about the perimeter?
Materials and Equipment
Here's a suggestion for your display: in addition to your background research and your proof, you can make a model of the Figure with colored paper. Use a compass and straightedge to construct the semicircles. Cut pieces of string or yarn equal to the arc-lengths of the semicircles. You can use these to demonstrate that the perimeter lengths are indeed equal. Repeat for 3 different measurements of semi circles.
Problems are not stop signs, they are guidelines. - Robert H. Schuller