March 14 is Pi Day. Mathematicians, teachers, and math geeks around the world celebrate.
Especially at 1:59. That’s when the date and time is 3/14 1:59 — pi to 5 digits.
My treat for you last year was a photo of pi decorated cookies. This year the treat is even more delicious — a Pi Song from Vi Hart and a Pi Limerick from me.
Vi Hart can sing!
You can’t deny Vi Hart has mathematical and creative talent. But who knew she had a musical voice!
Unfortunately she’s since taken that video down. 🙁
My Pi Limerick — because I can’t sing.
I can’t carry a tune in a bucket much less associate digits with musical notes.
But I can remember pi to 5 decimal places with the help of this limerick:
I’m a little anal when it comes to folding sheets. And it turns out I’m extremely good at it.
But until recently, I didn’t see that it had so much math in it.
Rip apart your sheets!
Okay, really — don’t.
But consider what it looks like if you tear out all the seams and remove the elastic. What you’re left with is a concaveirregular.
Check out this pseudo-infographic to see how easy it is to fold a concave irregular dodecagon:
Try it on your sheets.
The idea behind folding fitted sheets is the same. You can’t go about ripping out seams and tearing out elastic, but you can work around them.
And that’s what I did in this video:
Use it with your kids.
Practice folding your sheets my way, or just wad them up like many other people.
Either way, use the words “concave irregular dodecagon.” If your children question what you’re talking about, revel in your amazing intelligence, and encourage them to Google it.
If they’re young enough, just have them say it. Nothing’s cuter than a toddler saying fancy math words!
When Kate asked me this morning for “Spider Toast” I was stunned. What was I going to do with that request?
I pulled out some geometry and was able to convert a square into an eight legged spider!
It’s a great exercise for older kids to do for younger kids. It reinforces geometry and fractions, and everyone gets to have fun.
Start with a square — a piece of toast.
Unfortunately, bread doesn’t come in a variety of shapes. But with a knife, your’re armed to be creative with the geometry!
Toast your bread and spread cream cheese or peanut butter on it.
Use the steps below to cut out and assemble the Spider Toast.
Notice the geometry while making Spider Toast.
1. First, mentally divide the toast into thirds. Don’t cut anything yet.
2. Next, divide the toast into sevenths and cut out the shaded portions in the picture below.
In this step, you’re multiplying fractions. First we divided the bread into three pieces. Then we divided each of those into seven pieces to get 21 pieces. Each little rectangle is 1/21 of the bread.
This is a graphic representation of 1/3×1/7 = 1/21.
Make your Spider Toast face!
3. Assemble the cut-outs to be the face. If you center them just right, you’ll have 1/6 of the width of the bread left on both sides!
4. Smooth out the face so you can’t see the seams. Use blueberries for eyes and cut a crescent of cheese for the smile.
Go for it!
Make this morning nutritional, fun and educational! Add a glass of milk and a brief discussion of arachnids, and award yourself “Super Parent of the Day.”
And don’t forget to share how it went in the comments!
While at Dad 2.0 last weekend I intersected with Rob Rosenthal, the . His cook-off competition jersey had the number pi on the back. So you can imagine how I knocked everyone over to get to him.
I was instantly impressed with his “business card.” It was a Handy-Pal Pan Scraper. The perfect tool for any kitchen and a great way to make your mark if you write about kitchen things.
The Handy-Pal Pan Scraper is a square. Mostly.
When showing it to Husband, I noted that the Handy-Pal Pan Scraper’s corners were different.
My inner (comedic sidekick) voice said, “How different are they?”
(I ignored the invitation to create a goofy math joke.)
I looked at the Handy-Pal Pan Scraper more closely. All four corners were different.
My inner (smart) voice said, “What’s the angle on each corner?”
I ripped the thing from its package and traced it. I ran for the protractor.
Immediately after slapping the protractor down on my sketch I thought, “Duh – all angles are 90°.”
I needed a better question.
Clearly the question, “what’s the angle,” was not going to help me differentiate between the corners. And that’s what I really wanted — the legitimate answer to the question, “How different are the corners?”
I tried a few questions out, to see what would work:
How are the corners different? (too vague)
What’s the rounding difference? (what does that mean?)
What does it mean to be rounded differently? (attempting to clarify the previous question)
Round means a piece of a curve – like maybe a circle. Is each corner a piece of a circle? (this is starting to feel better)
Hey, it looks like each corner may be one fourth of a circle. So what’s the radius of each corner’s “quarter circle”? (gotcha!)
I had my question.
So it finally seemed, after all this internal conversation, that I had a question with a “non-duh” answer.
What is the radii of the corners?
I got out the ruler and started playing.
Turns out that each corner is indeed different than the others. My measurements are approximate. And close enough. 🙂
Say it out loud.
Do you have a Handy-Pal Pan Scraper in your kitchen? Take the opportunity next time you’re scrubbing a pan to point out that the corners have different radii.
I first saw this video over at MathFail. It’s cute, and I have to admit, kind of cool.
But anything this simplistic always sends me into skeptical mode.
Before we go any further, check it out:
Do you believe it?
This might be the question to start a discussion with a student. It’s certainly the first question that comes to my mind.
If it were really this simple, wouldn’t we have used it to “prove” the formula for the area of a circle much earlier?
What’s wrong with it?
For the “proof” in the video to work, you have to assume (or believe) that the circumference is 2πr. This seems a bit cheesy to me, since that formula is as complex as the one we’re trying to prove. Not to mention quite closely related. But I’ll let this one go.
The thing that really bothers me is that they use only a few chains — each of which has thickness.
If you filled the inside of a circle (a disk) with concentric circles, none of those circles would have a thickness. In fact there’s an infinite number of those circles.
Is it realistic to take each of those circles and fold them out and get a triangle?
Can you use it to teach?
I believe the makers of the video intended this to be a fun way to remember the area formula of a circle.
But the video would be better used to allow students to ponder the relationship of a circle to an isosceles triangle.
What do you think?
Are you okay with this video? Are you as skeptical as I am, or am I a little too sensitive?
I have long wondered about the similarity between some math words and some English grammar words. In particular ellipse vs. ellipsis and hyperbola vs. hyperbole.
I finally decided to look up their etymologies, and amazingly there is good rhyme to the reason!
Ellipse and Ellipsis
Both of these words come from a Latin root meaning, “a falling short or deficit.”
The grammar term, ellipsis, means the three dots used to designate missing words, or a deficit of words. Like … well…, you get the picture!
For the mathematical shape, or graph, an ellipse is created when a cone is cut by a line whose angle is less than (or falls short of) the angle of the side of the cone to the bottom of it. (#ARG, I know. Check out the pix.)
The brown line that creates the ellipse has a 25° angle which is much smaller than the 60° angle between the bottom and side of the cone:
You can see it “in action” here with the line falling:
Hyperbola and Hyperbole
A hyperbole is the fancy English grammar term for exaggeration. Everyone use hyperbole all the time! (See what I did there…?)
And a hyperbola in math is the graph/shape that looks like the light beams from a two-sided flashlight.
Both of these words come from a Latin word that means extravagance or “throwing beyond.” You can see how an exaggeration (a hyperbole) is throwing beyond. But what’s up with the math word, hyperbola?
We look to the angle of the cutting line again. A hyperbola is cut from a cone (actually stacked cones — see the picture) with a line who’s angle is “beyond” or more than the angle of the side of the cone to the bottom. It’s just the opposite of the ellipse!
Check it out: (This one is somewhat drawn to scale so you can really see what’s going on.)
Are there more?
These are the only two that have bugged me through the years. But now I’m wondering if there are other math words that have cousins over in the English department.
I started the ruler and compass series a while ago and am just now getting back to it. Here is my construction of a perpendicular bisector of a given line segment.
First, I drew a line segment:
Using my compass (which quickly gave out on me), I made two big fat arcs. They have the same radius — this is important.
Where those two cross, I drew a line. That line is the perpendicular bisector of the original segment (which means it makes a 90° angle and splits it into two equal parts):
Why does it work?
Well, that’s a great question. I’m sure there’s some proof of why this actually results in splitting the original line segment in half with a perpendicular line. I’ll have to think on it more.
But intuitively it totally feels right.
Now that’s a bad way to proceed with math, but it’s a great first start!
