Relatively Prime: Stories from the Mathematical Domain

Relatively Prime features stories and interviews from the mathematical world. Featuring math stories from people like Fields Medalists to indie rockers to linguists on topics ranging as wide as the artificial intelligence which defeated checkers and mathematics haiku battles. Relatively Prime has a mathematics story for anyone and everyone.


episode 41: 3 Scenes from the Life of Benjamin Banneker

On this month’s Relatively Prime Samuel shares three scenes from the life of Benjamin Banneker. One about a clock, one about a solar eclipse projectsion, and one about a puzzle. You can learn more about the life of Benjamin Banneker by checking out the book The Life of Benjamin Banneker by Silvio Bendini which was essential in the production of this episode and it is available to borrow for free on the Internet Archive or if you prefer a physical copy your library may have it on hand and if they do not the amazing system that is Interlibrary Loan should be able to provide for you.

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Chris Zabriske
Griffin Lundin
ᕲi̾r̾੮ Porcelai̾n


3 Scenes from the life of Benjamin Banneker

Scene 1: The Clock

It was only the second timepiece he had ever seen. And, to those of us alive today, the first we would have thought of as such, as this was a pocket watch and the other a simple sundial.

That Benjamin Banneker had never seen a watch before is not that surprising. After all he was a teenaged free African American man in the colony of Maryland in either the late 1740s or early 1750s. While there were a number of clockmakers who provided their works to farmers in the Chesapeake region, it will likely not come as a surprise that a family where the father is a freed slave and the mother the daughter of a freed slave and a formerly indentured servant were not among those clockmakers clients, though the family’s tobacco farm did allow them to be self-sufficient. The most likely thing is that Benjamin found a merchant or a traveler who not only owned a pocket watch but was willing to let a precocious free young black man take a good long look at it.

There is no historical evidence of what exactly Benjamin did when he set his eyes upon the second timepiece he had ever seen but we can make some educated guesses.

We can guess that he was able to get a good look at workings within. We can guess that he felt fascinated by these workings. We can guess his mind raced trying to understand how such workings were able to keep time so well that they could be relied upon. We can guess he wanted a clock of his own.

We can make those guesses because of what we know.

We know that after seeing the pocket watch Benjamin began to draw out the internal workings of gears and wheels and springs. We know he then worked on calculating the sizes and ratios needed to make a clock function correctly. And we know he used those drawings and calculations to make a clock all his own.

Fashioned primarily out of wood he carved himself, up to and including the gears, the clock Benjamin Banneker designed and built at 21 worked until he died at 74.

Scene 2: The Projection

More than 30 years of working the farm later Benjamin Banneker learns about, and quickly falls in love with, astronomy. At first it is only through occasional discussions with neighbor and noted amateur astronomer George Ellicott, likely with some nighttime telescopic adventures.

Never one to do things in half measure though, Benjamin wanted more. Which he got in 1788, when George offered to lend to him a telescope, some drafting instruments, and many astronomical texts. George also offered Benjamin lesson to help him through the texts and to learn to use the instruments. These lessons turned out to be unnecessary as Benjamin took to his Astronomical studies so vigorously that he worked through the texts before George to make his way back from an extended business trip.

Benjamin did not stop with going through some texts, no he moved right on to practical Astronomy. As well he should have considering it led him, a free African American man, in the newly minted state of Maryland to publish 6 Almanacs from 1792-1797 and to have a correspondence with Secretary of State Thomas Jefferson. But those happened later, and while impressive and great achievements there is a smaller one which tells us just as much about Benjamin Banneker.

Within the first year of receiving the texts and tools from George, Benjamin put to himself the task of making a projection of an eclipse of the sun. Using the tools at hand, his newly found knowledge and his skill at logarithmic calculation he completed his task which he eventually he sent it along to George Ellicott who was still away on business. George was understandably stunned that someone with whom he had left some books but not provided the lessons which should have been needed to understand them had produced such a work, so much so that the very small error in calculation the projection contained did nothing to lessen its sheen. Upon receiving George’s reply though Benjamin did not agree, he was distressed that he had made any error at all and endeavored to determine how such a thing could have happened. Which of course he did.

It turned out that Benjamin was using two books, one from James Fergusen and another from Charles Ledbetter, both of which had correct methods for projecting solar eclipses but which could lead to errors if they were used in conjunction with one another. Suffice it to say Benjamin did not make further errors in projecting solar eclipses.

Scene 3: Puzzle of the Dog and the Hare from from George Hopkins recorded, and solved, by Benjamin Banneker

When fleecy skies have Cloth’d the ground
With a white mantle all around
Then with a grey hound Snowy fair
In milk white fields we Cours’d a Hare
Just in the midst of a Champaign
We set her up, away she ran,
The Hound I think was from her then
Just thirty leaps or three times ten
Oh it was pleasant for to see
How the Hare did run so timorously
But yet so very Swift that I
Did think she did not run but Fly
When the Dog was almost at her heels
She quickly turn’d and down the fields
She ran again with full Career
And ‘gain she turn’d and the place she were
At every turn she gain’d of ground
As many yards as the greyhound
Could leap at thrice, and She did make,
Just six, if I do not mistake
Four times She Leap’d for the Dogs three
But two of the Dogs leaps did agree
With three of hers, nor pray declare
How many leaps he too to Catch the hare

Just Seventy two I did Suppose,
An Answer false from thence arose,
I doubled the Sum of Seventy two,
But still I found that would not do,
I mix’d the Numbers of them both,
Which Shew’d so plain that I’ll make Oath,
Eight hundred leaps the Dog did make,
And Sixty four, the Hare to take

That is all the time we have for this episode of Relatively Prime. If you want to learn more about the life of Benjamin Banneker may I suggest Silvio Bendini’s The life of Benjamin Banneker which is available to borrow on the Internet Archive or you can check your local public library and if they do not have it on hand may I suggest the amazing system that is Interlibrary loan. The music on this episode is from Chris Zabriske, Rodrigo Gonzalez, Griffin Lundin, Dirty Porcelain you can find links to their work in the show notes for this episode on
Also I want to be sure to thank all my patrons on Patreon. Without y’ll this episode and the lat 40 or so could not have happened so thank you. If you want to support the show like they do you can head over to and pledge whatever you can afford per episode.

Finally RelPrime is licensed under a Creative Commons attribution share-alike license so you can feel free to do whatever you want with the sounds on this episode as long as you say you got it from Relatively Prime and that you license it in the same way

Thank you all for listening and like the month before last and the month after this one I hope you have a matheriffic month. By y’all.


 2020-02-29  10m