475: Circle Theorems

Here are eight circle theorems, written by a Brit so you'll have to "translate" to American English ...
Are these the most important ones?
Are there any that are missing that you feel should be included in this group?

source:

Circle Theorems - these are very important to learn for the Higher Tier pic.twitter.com/rG4KOwwixP

— Corbettmaths (@Corbettmaths) May 31, 2015

474: Fractional Understanding

What insights does a student need to have before this problem is solvable?

473: Overlapping Squares

I might have posted this puzzle before.

What do your students think? Can they generalize it?
What is the overlapped area?

source:

As the red square is rotated around point O, what is the area of the overlap with the yellow square? #geomchat

— David Wees (@davidwees)

472: How Many geometry Theorems Are There?

That's pretty much it: How many Geometry Theorems are needed to solve this extended problem?

source:

Old Exam Questions #2 : My solution in a few days... http://t.co/VDHpuoDY5a pic.twitter.com/OFpD7AT6G4

— solve my maths (@solvemymaths) May 24, 2015

471: Digits in Fibonacci

We all recognize the Fibonacci Sequence:  1, 1, 2, 3, 5, 8, 13, 21, ...
What is the units digit of the sixty-first Fibonacci number?

Is there a pattern?

1,1,2,3,5,8,13,21,... What is the final digit of the sixty-first Fibonacci number?

— James Tanton (@jamestanton) May 24, 2015

470: Poor Alex Bellos

Normally, I'm glad when the nedia talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.

What's the error?

Oh, and solve it if you want, too. It's not really that hard.

Further questions:

• Which blanks CANNOT have a prime number in them?
• Which blanks COULD have certain prime numbers?
• Which blanks essentially force this problem to be non-unique?

source.
(answer linked from there)

469: Fix this Graph #ILostCount

This graph needs a lot of work.

What information is being presented?
What is the best way to display this information?
Does this graph rely too much on the reader's knowledge of the city?

source.