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### Patrick Honner

Shared publicly -Brought to you by the New York State Algebra exam.

http://mrhonner.com/archives/14706

But of course this is impractical, both for tests and for much of real world mathematics.

### Patrick Honner

Shared publicly -*“Four students are playing a math game at home. One of the math game questions asked them to write an algebraic equation.“*

Why invent such a ridiculous context for a math question?

Another installment in my review of New York State mathematics exams.

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What is the answer to this question?

A.) All of the above

B.) None of the above

C.) All of the above

D.) None of the above

### Patrick Honner

Shared publicly -https://ds3.research.microsoft.com/

### Patrick Honner

Shared publicly -https://www.youtube.com/watch?v=TAPoNXrWNMc

### Patrick Honnerowner

Discussion -- General - Here are two posts of mine about Cavalieri's Principle:

http://mrhonner.com/archives/4000

http://mrhonner.com/archives/3665

And the Wikipedia entry contains the classic application of the principle: deriving the formula for the volume of a sphere.

### Patrick Honnerowner

Homework -- Geometric Dissections - **Workshop 2 -- Problem 5**

Prove the angle sum formula for sine.

**Extension**Do so using Euler's formula!

http://www.cut-the-knot.org/triangle/SinCosFormula.shtml

### Patrick Honner

Shared publicly -### Patrick Honner

Shared publicly -Tons to learn about food, cooking, and shopping from Alan Eliasen as he blogs about his 45-day challenge.

https://futureboy.us/blog/twofifty.html

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*thinking*is to their lives. It can branch out, too. Like, I usually pick my own berries to freeze for the winter, which saves us a lot money, but those are hours I'm not working and therefore not earning money. But then there are social and ecological benefits hard (yet somewhat possible) to quantify.

### Patrick Honner

Shared publicly -To be honest, I don't love pi day. I think a lot of the activities are kind of goofy and non-mathematical. However, I honestly love the number pi—its mathematical connections and its history. So my presentation was a mathematician's take on pi. I'm very happy with how it went.

I talked about the history of pi (and I stated my belief that we should call pi "Archimedes's number"). We talked about how to calculate digits of pi. I had them compute some approximations from polygonal approximations to circles. I told them about Archimedes's 96-gon and Van Ceulen's 2^(62)-gon approximations.

Rather than calling pi "an infinite number" (which it isn't) we talked about rational and irrational numbers and what their decimal representations look like.

We had a few pi-related activities (like: if one string is wrapped around the equator and a second string is around the equator but one foot off the ground, how much longer is the second string?)

I talked about the importance of proof in mathematics, and I gave a sketch of the proof that if C=2πr, then A=πr^2. (I also tried to impress upon them how cool and surprising it is that this same number appears in both formulas.)

Finally, I told them that the book of mathematics is not yet finished. We are still making new discoveries and there are proofs still to be discovered. For example, we still don't know if pi is "normal"—roughly speaking, that there are the same fraction of 0's as 1's as 2's as 3's... in the decimal expansion.

We ate pie afterward. Some of the kids brought in pie—including this one that my wife and son made (please don't tell them that the last digit is wrong...).

As a side note: if you have the opportunity to go in and speak to your kids' class—do it! It is extremely fun and rewarding. They have so many great questions and comments. Their enthusiasm is unbelievable. I do it every year, and I love it—and I think the kids do too.

### Patrick Honnerowner

Homework -- Geometric Dissections - Notice the amazing relationship between dihedral angles in the tetrahedron and square-based pyramid: glue them together and they become coplanar!

### Patrick Honnerowner

Homework -- Geometric Dissections - **Workshop 2 -- Problem 6**

Find all the dihedral angles in the following solids.

- NYC DOETeacher, present

- University of Wisconsin-MadisonMathematics
- Wayne State UniversityMathematics, Philosophy

Tell Me Why You Blog function-of-time.blogspot.com So, as much to my surprise as anyone's, I'm not only talking at NCTM in April but they made me a featured speaker? Only freaking out a littl |

What do we learn from our students? anglesofreflection.blogspot.com It's been a while--partly because of work, and partly because I just found out about the death two summers ago of one of my former students, |

Mathematical Association of America plus.google.com The largest professional society that focuses on mathematics accessible at the undergraduate level. |

Google+ market.android.com FEATURES:- New Feature: Google+ Communities - Enjoy magazine style layout in the new tablet version - Automatically share photos to an Event |

Math Photo: Sculpture of Spheres « Mr Honner mrhonner.com Skip to content. Home · Sample Page · Table Number · Hits and At-Bats · 837751 · Hardest Word to Guess · Brooklyn to Burlington · Math and L |

Math Photo: Straw Cylinders « Mr Honner mrhonner.com Skip to content. Home · Sample Page · Table Number · Hits and At-Bats · 837751 · Hardest Word to Guess · Brooklyn to Burlington · Math and L |

Math Art: Kolam Spirals « Mr Honner mrhonner.com Skip to content. Home · Sample Page · Table Number · Hits and At-Bats · 837751 · Hardest Word to Guess · Brooklyn to Burlington · Math and L |

Math Art: Starburst, by Tim Locke « Mr Honner mrhonner.com |

White Group A level JC H2 Maths tuition: 92nd Carnival of Mathematics www.whitegroupmaths.com Ninety-two isn't any ordinary number; it is associated with "royalty". How does that work out? It represents the number of solutions to whic |

Math Art: Student Sliceforms « Mr Honner mrhonner.com |

Math Photo: Sharp Tangency « Mr Honner mrhonner.com |

9/15/12 — Happy Right Triangle Day! « Mr Honner mrhonner.com |

The Algebra of Coffee Consumption « Mr Honner mrhonner.com |