## Wednesday, March 29, 2017

### Height and Steps

The other night I watched an episode of the Librarians.  The girl with something in her brain who could see all her senses input made a comment about telling the size of a set based on the number of steps the actor takes to cross a set if you know the actor's height.

While researching this comment, I came across a really interesting article in Scientific American on estimating a person's height from the length of their walk.

The article began with discussing some interesting ratios I hadn't realized.  For instance, if you have your arms completely outstretched, the distance between the tips of your hands is about equal to your height. The length of a person's legs is related to their height as a ratio.

One of the activities you can do to find it is to measure out 20 feet in a flat area like a hallway or cement walkway.  Mark the beginning and end.  Measure the height of each walker.  Have them walk the 20 foot length. Count the number of steps it takes them to reach the end.  Determine the length of their stride by dividing the 20 foot length by the number of steps it took them.  Then divide the stride length by their height, both numbers should be in feet.  The answer for all walkers should be about .40.

So if you have the length of a person's stride, you can divide it by about .43 to get their approximate height. The answer won't be exact but it will be close.  .43 is considered to be an average.

Other interesting ratios include:
1.  You are about 1 cm taller in the morning after sleeping all night.  You shrink a bit during the day.  Imagine being able to have students measure themselves first thing in the morning and last thing at night.  Students could calculate the 1 cm as a percent of their total body height so they'd know their "shrinkage factor."

2. The ratio of the femur bone to the height is interesting.  It is about 1/4th your height.  You could use this to discuss how forensic scientists determine the height of the person whose bones were found.  A practical use.

3. Another interesting ratio is the head to the body which turns out to be change depending on the age of the person.  A small child has a 1 to 4 ratio while an adult usually has a ratio of 1 to 8.

Finding these ratios could be easily done in the classroom by having students carry out an experiment of two.  Scientific American has two different pages with everything you need to have students learn about these ratios themselves.  One is the Human Body Ratios page while the other is Stepping Science finding the height of a person based on their stride.

These exercises would be great when teaching about ratios because these ratios are ones they can easily relate to.  Let me know what you think.  I'd love to hear from you on this.  Thanks for reading.