Arm span to height, Head span to height?

To compare the length of different parts of your body to your height, we will first create a string the length of your height. Take off your shoes. The easiest way is to lie on the ground with your heels pressing against a wall. Look straight up and have your helper place a hardcover book flat on your head, resting on the ground. Get out from under the book and, together, span the yarn across the floor from the wall to the book. Cut the yarn just where it reaches the book. Now, you have a piece of yarn that is as long as you are tall. If lying on the ground is not possible, you can also stand flat on the floor against the wall and have the book rest against the wall.

First, we examine your arm span-to-height ratio. Your arm span is the distance between your fingertips when you stretch your arms out as far as they can reach. How do you think your height compares to your arm span? Would it be similar, way longer, or way shorter?

Now, stretch your arms out as far as they can reach. Your arms will be parallel to the ground. Hold one end of the piece of yarn you just cut off with the fingertips of your left hand. Let your helper span the yarn towards the tip of your right hand’s middle finger. Is piece long enough, way longer, or way too short? What does this tell you about how your arm span compares to your height?

For most people, their arm span is about equal to their height. Mathematicians say the arm span-to-height ratio is 1 to 1: your arm span goes 1 times into your height.

Now, let’s explore another ratio: the length of your femur bone to your height. The femur bone is the only bone in your thigh. To measure its length, sit down and span a new piece of yarn over your thigh from the hip joint to the edge of your knee, and cut the yarn there.

Make an estimate. How many times would this piece of yarn go into the piece that is as long as you are tall? Can you find a way to test your estimate?

There are several ways to compare the length of the two pieces of yarn. You might cut several pieces of the length of your shorter string, lay them end-to-end next to your longer piece, and count how many you need. Another way is to fold the longer string into equal parts so that the length of the folded string equals the length of the shorter string. The number of folds needed is exactly the number of times your shorter string goes into your longer string.

Did you see that the length of your femur bone goes about four times into your height? You can also say that if you divide your height in four equal pieces, you have the length of your femur bone, or the length of your femur bone is one fourth of your height. Mathematicians call this a 1 to 4 ratio.

Now, let’s move on to a ratio that might help you make more realistic drawings: the head-to-body ratio. How many times would the length of your head fit into your height? Maybe four, six, or eight times? To test six times, fold the yarn with length equaling your height into six equal pieces. Have your helper place a book flat on your head and hang the folded string from the side of the book. If the other end of the string is about level with your chin, your height would be about six times the length of your head, or your head-to-body ratio would be 1 to 6. Which number of folds fits best for you?

There are many more body ratios you can explore, like the circumference of your head compared to your height, the length of your forearm to the length of your foot, or the length of your thumb to the length of your hand. Use pieces of yarn to measure, compare, and detect these and/or other ratios of your body.