Project C03 - Ratios and Proportions Project C03 - Ratios and Proportions

You will begin this project by making several measurements. All measurements should be in centimeters and rounded to the nearest 0.5 cm. Follow the directions below when making the measurements.

A. Height and navel to floor: Measure without shoes.
B. Tibia: Rest the foot on the floor and measure from the ankle bone to the top of the tibia on the outside of the kneecap.
C. Radius: Rest the elbow on the desk with the hand up and measure from the tip of the elbow to the wrist bone.

Name of Person     Height     Navel to Floor     Tibia         Radius    
                   
                   
                   
                   

  1. Use you calculator to compute decimal equivalents for each of the following ratios. Round each decimal number to the nearest thousandth.

    Name of Person [height/ navel to floor] [navel to floor/ height]     [tibia/ height]         [radius/ height]    
                       
                       
                       
                       

  2. Compare the numbers in each column of the table. Which ratios are approximately the same for all people?
  3. Find the average of the decimal values for the tibia to height and radius to height ratios. You may include data from other groups.
    1. The length of the tibia is approximately what fraction of the height?
    2. The length of the radius is approximately what fraction of the height?
  4. At the famous French Neandertal burial site at Régourdou, paleoarchaeologists have unearthed the remains of several early humans.
    1. Scientists believe that a certain 37 cm tibia and a 27 cm radius belong to the same individual. Based on the data that you've collected from modern humans, what do you think? Explain.
    2. Scientists have discovered a 32 cm radius and certain evidence suggests that it belonged to a female. What do you think? About how tall would have she been?
  5. Find the average of the decimal values for the height to navel-to-floor and navel-to-floor to height ratios.
  6. The average ratio for height to navel-to-floor for all humans is approximately 1.618. Compare this decimal with the average from your group.
  7. Write the reciprocal for 1.618 rounded to the nearest thousandth. What did you find? (Extra Credit: Find all decimal numbers with this property.)
  8. Research the Golden Ratio. Write a paragraph or two about this number and how it arises in applications.
This project was adapted from an activity in Mathematics Activities for Elementary School Teachers: A Problem Solving Approach, 3rd Edition by D. Dolan, J. Williamson, and M. Muri.

File translated from TEX by TTH, version 1.98.
On 26 May 2000, 08:26.