Puzzle: Patty Paper Trisection

Posted on by Denise Gaskins

[Feature photo above by Michael Cory via Flickr (CC BY 2.0).]

trisection

One of the great unsolved problems of antiquity was to trisect any angle using only the basic tools of Euclidean geometry: an unmarked straight-edge and a compass. Like the alchemist’s dream of turning lead into gold, this proved to be an impossible task. If you want to trisect an angle, you have to “cheat.” A straight-edge and compass can’t do it. You have to use some sort of crutch, just as an alchemist would have to use a particle accelerator or something.

One “cheat” that works is to fold your paper. I will show you how it works, and your job is to show why.

Continue reading Puzzle: Patty Paper Trisection

Historical Tidbits: Alexandria Jones

Posted on by Denise Gaskins

[Read the story of the pharaoh’s treasure: Part 1, Part 2, and Part 3.]

Here are a few more tidbits from math history, along with links to relevant Internet sites or books, and three more math puzzles for you to try. I hope you find them interesting.

Next time, a new adventure (sort of)…

Continue reading Historical Tidbits: Alexandria Jones

The Secret of the Pharaoh’s Treasure, Part 3

Posted on by Denise Gaskins

[In the last episode, Alexandria Jones discovered a mysterious treasure: three wooden sticks, like tent pegs, and a long loop of rope with 12 evenly spaced knots. Her father explained that it was an ancient Egyptian surveyor’s tool, used to mark right angles.]

Back at the camp, Fibonacci Jones stacked multi-layer sandwiches while Alexandria poured milk and set the table for supper.

“Geometry,” Fibonacci said.

“What?”

“Geo means earth, and metry means to measure. So geometry means to measure the earth. That is what the Egyptian rope stretches did.”

Alex thought for a moment. “So in the beginning, math was just surveying?”

“And taxes…”

Continue reading The Secret of the Pharaoh’s Treasure, Part 3

Geometry: Can You Find the Center of a Circle?

Posted on by Denise Gaskins

Is it possible that AB is a chord but NOT a diameter? That is, could circle ABC have a center that is NOT point O?

For the last couple of days, I have been playing around with this geometry puzzle. If you have a student in geometry or higher math, I recommend you print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

[MathNotations offers many other puzzles for 7-12th grade math students. While you are at his blog, take some time to browse past articles.]

The Secret of the Pharaoh’s Treasure, Part 2

Posted on by Denise Gaskins

[In the last episode, Alexandria Jones, daughter of the world-famous archaeologist, caught her father’s arch-enemy trying to uncover the Pharaoh’s Treasure.]

…”I can’t believe it!” Simon Skulk threw down the last stone in disgust and walked away. At the mouth of the cave, he turned back and shook his fist. “You haven’t seen the last of me, Alexandria Jones.”

Her muscles aching, Alex sank to the ground and hugged her dog. The she gave him a little push toward the front of the cave. “Rammy, go get Dad.”

Ramus barked once and took off running.

Alex turned back to look at the Pharaoh’s Treasure. Where the last stone had stood was a hole. In the hole lay three wooden sticks, like tent pegs, and a long loop of rope with 12 evenly-spaced knots.

What could it be?

Continue reading The Secret of the Pharaoh’s Treasure, Part 2

Carnival of Mathematics, ordinal 5

Posted on by Denise Gaskins

Carnival of MathematicsI missed getting an entry into the latest Carnival of Mathematics, which went up a day early at Science and Reason. (Serves me right for procrastinating!)

As usual, most of the articles are well over my head.

The carnival begins with a tribute to Field’s Medalist Paul Cohen (April 2, 1934 – March 23, 2007), the man who settled the first of the famous Hilbert Problems, the Continuum Hypothesis. Then come the math articles.

Here are my favorites:

  • The old new math
    In which JD teaches his algebra class a bit of twentieth-century history. If you aren’t familiar with Jonathan’s blog, be sure to spend some time browsing his “puzzle” posts.

All Odd Numbers Are Prime — A Corollary

Posted on by Denise Gaskins

[Rescued from my old blog.]

Once again, Rudbeckia Hirta brings us some funny-but-sad mathematics. The test question was:

Without factoring it, explain how the number
N = (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11) + 1
can be used to argue that there is a prime number larger than 11.

Continue reading All Odd Numbers Are Prime — A Corollary