Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.
Puzzle: Figuring Out Figurate Numbers
Photo by frumbert.
Alexandria Jones‘s parents decided that the family needed to relax after the excitement of tracking Simon Skulk, so they spent the next day at a beach on the Mediterranean coast. Leon collected pebbles and tried to build up figurate numbers — numbers that make a figure, or shape — the way Dr. Theano had shown them.
The Puzzling Pythagorean Pebbles
Alexandria Jones and her family flew to Italy for spring break. Her father, the famous archaeologist, had to visit an excavation.
It was late when their plane landed in Crotone, a small coastal city near the instep of Italy’s boot. Dr. Jones had used the Internet to find a hotel that allowed pets, so Alex was able to snuggle down with her favorite pillow — her trusty dog, Ramus.
The Original School of Mathematics
The next day, Dr. Jones introduced his family to Sonya Theano, a former student of his and the director of this dig. “Come, let me show you around,” Dr. Theano said. “We’ve uncovered several buildings of a small compound, set apart from the city of Crotona, as it was called then. From the pottery and trade goods, we estimate these buildings were in use around 550-500 BCE.”
Retro-Dated Magic Square Puzzles
The hectic holidays kept me from finishing the Christmas stories of Alexandria Jones. I am finally getting them typed up, but I past-dated them to keep the seasonal connection. So if you want to read more, here are the newest posts:
Answers to Alex’s and Leon’s Puzzles
Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original posts. Figure them out for yourself — and then check the answers just to prove that you got them right.
Alex’s & Leon’s Homeschool Puzzle
While checking out the book table after a homeschool group meeting, Maria Jones glanced up to see her children laughing with some kids she did not recognize. Driving home, she asked about the new family, but Alex and Leon had been too busy exchanging silly stories to even ask the strangers’ names.
“Well,” Leon said, “the boy told me he has twice as many sisters as brothers.”
No way!” said Alex. “The girl told me that she has the same number of brothers and sisters.”
How can that be?
Leonhard’s Block Puzzles
Leonhard Jones is Alexandria Jones’s younger brother. He enjoys woodworking, and he cut a wooden cube into 8 smaller blocks to make himself a puzzle.
Puzzle #1
Leon painted the 8 blocks with his two favorite colors: red and forest green. When he was finished, Leon could put the blocks together into a red cube, or he could switch them around to make a green cube.
How did Leon paint his blocks?
Egyptian Fractions: The Answer Sheet
Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer (relatively) soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.
The Secret of Egyptian Fractions
Alex made a poster of Egyptian-style fractions, from 1/2 to 9/10. Many of the fractions were easy. She knew that…
Therefore, as soon as she figured out one fraction, she had the answer to all of its equivalents.
She had the most trouble with the 7ths and 9ths. She tried converting these to other fractions that were easier to work with. For example, 28 has more factors than 7, making 28ths easier to break up into other fractions with one in the numerator.
The Secret of Egyptian Fractions
Photo from Library of Congress via pingnews.
Archaeology professor Dr. Fibonacci Jones came home from a long day of lecturing and office work. Stepping inside the front door, he held up a shiny silver disk.
“Ta-da!” he said.
“All right!” said his daughter Alexandria. “The photos are here.”
They had to chase Alex’s brother Leon off the computer so they could view the images on the CD, but that wasn’t hard. He wanted to see the artifacts, too. Alex recognized several of the items they had dug up from the Egyptian scribe’s burial plot: the wooden palette, some clay pots, and of course the embalmed body.
Then came several close-up pictures of writing on papyrus.
Photo from MathsNet.net.
How to Write Egyptian Fractions
“I remember how to read the Egyptian numbers,” Alex said, “but what are these marks above them?”
Dr. Jones nodded. “I thought you would catch that. Those are fractions. The scribe places an open mouth, which is the hieroglyph ‘r’, over a number to make its reciprocal.”
“I know that word,” Leon said. “It means one over the number. Like, the reciprocal of 12 is 1/12, right?”
“That is right. 1/12 would be written as…”
The Rest of the Story
As I transcribed this article from my old math newsletter, I realized that it would require more graphics than I was willing to construct. LaTex does not handle Egyptian hieroglyphs — or at least, I don’t know how to make it do so. Instead, I decided to scan the newsletter pages and give them to you as a pdf file:
Right-click and choose “Save” to download:
- The secret of Egyptian fractions (pdf 364KB)
The file includes a student worksheet for Egyptian fractions from 1/2 to 9/10.
Egyptian Fractions: The Answer Sheet
The answers are now posted.
To Be Continued…
Read all the posts from the January/February 1999 issue of my Mathematical Adventures of Alexandria Jones newsletter.
Christmas Puzzle Answers
Remember the Math Adventurer’s Rule: Figure it out for yourself! Whenever I give a problem in an Alexandria Jones story, I will try to post the answer soon afterward. But don’t peek! If I tell you the answer, you miss out on the fun of solving the puzzle. So if you haven’t worked these problems yet, go back to the original post. Figure them out for yourself — and then check the answers just to prove that you got them right.
