Whose Foot Is a Foot?

Whose Foot Is a Foot? — page 3 — SO MANY MEASUREMENTS WITHIN SIX MONTHS A BABY TYPICALLY DOUBLES ITS BIRTH WEIGHT LOOKING BACK ON ALL THE MATH YOU HAVE EVER DONE WHEN DO YOU THINK YOU STARTED The very first time you were involved in a calculation was likely right after your birth Even though you can’t remember it it was important One of the first things that happens after a baby is born is that their length and weight are taken Such information is among the first facts that friends and family receive about a baby the first math that you were ex It’s fitting that measurement is posed to since math ematicians have been measuring quantities for hundreds of years For example when mathematicians first started do ing math they didn’t understand numbers as being representations of quantities If they wanted to talk about the number two they would reference a stick or segment that was two units long As a result metrology the study of measure ment has always been around and is closely related to all other branches of math The confusing part about using 6

Whose Foot Is a Foot? — page 4

Whose Foot Is a Foot? — page 5 — units to stand for numbers was that mathematicians in different parts of the world had different names for their units You probably have heard of units such as yards meters liters and pounds But do you know what a cubit palastai or digitus is They may sound like strange words but they are used for measuring the lengths of different objects A cubit was an Egyptian unit defined as the distance from the elbow to the fingertips A palastai was a Greek measurement comparable to the size of a person’s foot A digitus was a Roman measurement equal to the width of a finger Many other units for measuring volume or weight were also used in those ancient civilizations Did you notice a common theme in how those lengths were defined If you recognized that the human body was the basis for the mea surements you would be correct In fact features of the human body have served as standards for units of length in civilizations the world over Can you think of any problems that could result from measuring like that As Egyptians began building pyramids they realized there were some problems with the cubit They figured out that the standard was THESE IMAGES ILLUSTRATE A CUBIT BELOW LEFT AND DIGITUS RIGHT 8

Whose Foot Is a Foot? — page 6 — not so reliable because the length of one person’s arm might not nec essarily match the length of another’s As a result their cubits might vary That would affect the execution of a construction plan especially one involving as many pieces of precisely cut stone as a pyramid So the Egyptians took a piece of granite and made a royal standard for the cubit Then copies were made of that piece so that all measurements having to do with cubits would be the same Although body parts worked well enough for measuring smaller units they weren’t adequate when it came to distances As civilizations traveled to new areas and attempted to capture the scale and scope of the world on maps they needed ways of representing long distances Measuring with the width of a finger wasn’t going to work The Romans had a standard that they began using in the fourth cen tury They defined a length called a pede which was very similar to our foot measurement Five pedes were equal to 1 passus a pace or stride and there were 1,000 passuum in a mile Essentially the Roman mile was approximately 5,000 feet That works out to be almost nine-tenths of a current American mile or one and a half times a kilometer FIVE PEDES WERE EQUAL TO ONE PASSUS 9

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