Tag Archives: Euclid

The big ditch

A passenger barge pulled by a mule or two. The helmsman steers.

The cities on the eastern coast of the United States needed to be connected with the western settlements so that both could do business. One of the first ideas to shorten the trip from New York City to Ohio was the wonderful Erie Canal.

An upstate New York miller named Jesse Hawley suggested digging a long ditch, a canal, from the Hudson River at Albany to the Great Lakes at Buffalo. Even President Jefferson thought it was a crazy idea, but New York Governor Dewitt Clinton liked it and pushed through government funding for construction. For eight years—from 1817 to 1825—crews worked to dig the canal. It was an engineering marvel. How did they figure out how much dirt needed to be moved, or how much of a slice to take out of hill? From what I understand, there was never an accredited engineer on the building site. Back in those days, presumably, a kid’s grade school education included Euclid’s Elements (I’m not kidding. Up until 100 or so years ago Elements was the #2 bestseller after the Bible).

When the canal was done, you could get to the MidWest from New York City in less than half the time of a stagecoach.

“Canal packet boat passengers traveled in relative comfort from Albany to Buffalo in five days—not two weeks in crowded stagecoaches. Freight rates fell 90 percent compared to shipping by ox-drawn wagon. Freight boats carried Midwestern produce from Buffalo to Albany. Most continued on to New York City’s seaport, towed down the Hudson River in fleets behind steam tugboats. Mid-western farmers, loggers, miners, and manufacturers found new access to lucrative far-flung markets.”

This site has a really good video about the canal—https://eriecanalway.org/learn/history-culture

Here’s Bruce Springsteen singing the Erie Canal song—


Archimedes and his odometer

Archimedes was a Greek mathematician who specialized in measuring space. He was certain that there must be a way to accurately measure how much space is in a circle—area—or how much space is in a sphere or a cylinder—volume (he figured out how to measure volume when he noticed that a certain amount of water spilled out when he got into a bath tub). Archimedes was influenced by other great mathematicians, like Pythagorus and Euclid.

Archimedes invented many wonderful machines, like a screw for drawing up water, or catapults that were used to fight off invading navies. Although we don’t have his plans for it, Archimedes is said to have invented a way to measure distance. This machine is called an odometer.

Archimedes’ odometer operated on the idea that every time a wheel goes around, it travels its own circumference. The odometer adds up those circumferences and marks when the wheel has traveled a mile. In our last post, we showed how a standard Roman chariot wheel goes around 42 times to travel a mile.

We know about Archimedes’ odometer because the Roman military engineer Marcus Vitruvius Pollio (80–70 bc – 15 bc), or Vitruvius for short, wrote about it in his 10-volume book De Architectura. Engineers build stuff. As the Roman Empire expanded, the army took along a corps of engineers to build fortifications; siege engines; bridges; tunnels; aqueducts to provide water; and roads. These engineers did such a good job that you can still find Roman bridges, aqueducts and roads today.

Emperor Caesar Augustus wanted to know exactly how big the empire was and decreed that mile markers should be put up along the newly-built roads. Vitruvius decided to build Archimedes’ odometer to accurately measure the miles.

We only know what Vitruvius’ odometer looked like from a fanciful drawing. We don’t know exactly how it worked. Some people, including Leonardo da Vinci, have come up with some pretty good guesses about how it worked. You can see Leonardo’s drawings here—plus, you can even download plans if you’d like to build one yourself! Now that’s cool.

We do know that every time the chariot wheel goes completely around, it moves other gears. The other gears are set up to mark a mile at the 42nd revolution of the chariot wheel. The trick is gear ratio—meaning some gears are bigger, some gears have more teeth. If the gear on the drive shaft has only one tooth and the gear holding the marbles has 42, the marble-gear moves 1/42 of a revolution every time the chariot wheel goes completely around. At the 42nd revolution, a hole with a marble lines up with a hole underneath the gear and the marble drops into a bucket. Each dropped marble represents one mile traveled.



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