Some more information can be found here (look in the description of the video). A second spoiler video can be found here.
Pole to Pole Run
Utterly awesome.
Skallops – Geometry Heaven
Skallops are a construction toy that uses laser (no sharks) cut wood clips to put together playing cards. They are up on kickstarter now and they can make some incredible shapes. I just ordered a set myself.
Paper #wcydwt
Neat video:
Note: All photos were printed on recycled paper. Wasn’t that nice of them.
So how many photos? Answer found here.
IB Thoughts?
So our school is looking into implementing the International Baccalaureate program at our school in addition (?) to our AP programs. I know little about IB, and I’m interested in your knowledge and opinions on the IB program. Lemme have it. Good stuff? Things to watch out for?
Fibonacci and Recursion
To introduce the fibonacci sequence using the recursive series to my Pre-Calc H class (although most of them know it), I came up with something on the fly that worked nicely. To set up the fibonacci sequence, I showed them a recursive program that calcuates the sequence in a very clear (but inefficient) way.
def fibonacci(n):
if n==1:
return 1
elif n==2:
return 1
else:
return fibonacci(n-1)+fibonacci(n-2)
for number in range(1,10):
print "fibonacci number " + str(number) + " is ",
print fibonacci(number)
This is probably the first time they’ve seen programming in person, so to make it real I gave a post-it to each student and then had them stand up in a line. I had the person at the start of the line write n=1 on their post-it, and then they continued to the end of the line, n=19. I gave the first two students in the line their fibonacci numbers 
Then I asked the person at the end of the line what his fibonacci number was (
Well this continued all the way back to the start, and then after 
…
To show the class how inefficient the above algorithm is, I calculated 
The Code:
def fibonacci(n):
if n==1:
print "Sage"
return 1
elif n==2:
print "Jessica"
return 1
else:
return fibonacci(n-1)+fibonacci(n-2)
print fibonacci(19)
The Output (Click to expand, but it’s very long. An interesting number of lines *hint*):
Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage Jessica Sage Jessica Jessica Sage 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So that algorithm is very inefficient for calculating fibonacci numbers because it has no memory of the previous fibonacci numbers. When
Finally to cap it off, talk about the ratio of the fibonacci numbers that you’ve written on the board. These numbers tend towards the golden ratio (
Awesome.
Continue deep into math teacher land talking about phi and fibonacci numbers. Possibly share an applet like the following which shows that phi is present in seed growth in plants like sunflowers.
Seedhead.
Or show (or assign) a video about the Golden Ratio and Fibonacci like Keith Devlin’s talk where he discusses what is true and what is false about the golden ratio.
Cheers.
Dan
Dr. Square
Much like the Collatz conjecture, the Dr. Square Puzzle (from the blog mathforlove) is an intriguing problem.
With some playing around, we came up with what I think is an excellent (and solvable) puzzle. He dubbed it the Dr Square puzzle, because it involves one of the steps in taking the digital root (dr) and squaring numbers. Here’s how it goes.
Step 1: Choose a starting number.
Step 2: Square the number.
Step 3: Sum up the digits of that number.
Step 4: Repeat steps 2 and 3 until you understand what’s going on.
Example. Let’s take the number 26. Squaring it gives 676. The digital sum of 676 is 19. Squaring gives 361. Digital sum of 361 is 10. Squaring 10 gives 100. Digital sum of 100 is 1. Squaring gives 1. Digital sum gives 1. So we stay at 1 forever once we get there.
More briefly, we could write 26 –> 676 –> 19 –> 10 –> 100 –> 1 –> 1 –> 1 –> etc.
Naturally, I wrote a python program to check the first million number and so far it looks like they are right. If you take off the comment symbol (#) from lines 6, 20, 23, and 24 then it will print the path to each number.
Geogebra Dynamic Conics for PreCalc
For Precalc H, I created a series of dynamic Geogebra files, where the teacher or student uses sliders to control the center and the a (and b) values of the conic. The file calculates and graphs the appropriate conic, foci, directrices, etc.
All the files can be downloaded here.
Sample:
Or you can go to geogebratube to run them in your web browser.
Circle
Ellipse (wide) and Ellipse (narrow)
Hyperbola (Left and Right) and Hyperbola (Up and Down)
Parabola (Function) and Parabola (Not a function)
Cheers.
Puzzler : 20,000 Lights
From Car Talk.
RAY: This puzzler is from my “ceiling light” series. Imagine, if you will, that you have a long, long corridor that stretches out as far as the eye can see. In that corridor, attached to the ceiling are lights that are operated with a pull cord.
There are gazillions of them, as far as the eye can see. Let’s say there are 20,000 lights in a row.
They’re all off. Somebody comes along and pulls on each of the chains, turning on each one of the lights. Another person comes right behind, and pulls the chain on every second light.
TOM: Thereby turning off lights 2, 4, 6, 8 and so on.
RAY: Right. Now, a third person comes along and pulls the cord on every third light. That is, lights number 3, 6, 9, 12, 15, etcetera. Another person comes along and pulls the cord on lights number 4, 8, 12, 16 and so on. Of course, each person is turning on some lights and turning other lights off.
If there are 20,000 lights, at some point someone is going to come skipping along and pull every 20,000th chain.
When that happens, some lights will be on, and some will be off. Can you predict which lights will be on?
I created a Python program that prints the lights that are on (I got stumped trying to figure it out, and for some reason this method was easier for me). Found here.
Cartalk Puzzler – Stone Temple Farmers
From Cartalk.
Stone Temple Farmers
RAY: A farmer had a 40-pound stone that he could use to weight 40 pounds of feed, hay, or whatever else he wanted to sell from his farm. He had a balance scale, and he put the stone on one side and piled the other side with feed or hay, and when it balanced, he knew he had 40 pounds.One day, a neighbor borrows the stone, but he had to apologize when he returned it, broken into four pieces. The farmer who owned the stone later told the neighbor that he actually had done him a favor. The pieces of the broken stone could now be used to weigh any item, assuming those items were in one-pound increments, from one pound to 40.
The question is, what were the weights of the four individual stones? And if you want to weigh one pound, six pounds, 11 pounds, 22 pounds, 39 pounds — how would you use the stones, the thing you are weighing, and the balance scale?
And here’s the Hint: how would you weigh two pounds?
Well?