Challenge

The Shape of the Moon’s Orbit

This is a short and readable exploration of the question “What is the shape of the Moon’s orbit around the Sun?”

http://www.math.nus.edu.sg/aslaksen/teaching/convex.html

The Moon makes circles (ellipses, really) around the Earth while the Earth makes circles around the Sun, so what does the path of the Moon look like?

It’s a fun problem to think about, and I encourage you to do just that before you click through and see the discussion.

This simply posed problem touches on polar and parametric curves, 3-dimensional geometry, and of course, astronomy. And naturally there are lots of extensions, like “What if something were orbiting the Moon?”

By patrick honner, 13 years4 years ago

Challenge Resources Teaching

Street Fighting Mathematics

Sanjay Mahajan’s Street Fighting Mathematics is a short, dense, and engaging book that explores some mathematical problem-solving techniques not typically taught in math class.

These techniques, favored by engineers and scientists who are usually more interested in the answer to a question than in the mathematical theory that gets them there, can turn seemingly intractable problems into simple ones, often just by a change in perspective.

For example, the book offers a short treatment of Feynman’s differentiating-under-the-integral approach, one of the more famous “back of the napkin” techniques. Mahajan even “guesses” the definite integral that yields the area under the bell curve, using dimensional analysis the likes of which I’ve never seen.

A “Street Fighting Mathematics” course is offered through MIT’s OpenCourseWare, which includes lectures, notes and problem sets. In addition, Mahajan has made the book available for free in PDF format.

By patrick honner, 13 years4 years ago

Challenge NYT

Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:

https://learning.blogs.nytimes.com/2012/01/11/test-yourself-math-jan-11-2012/

This problem is related to worldwide caviar production. What is the total worth of all the caviar produced in the world in one year?

By patrick honner, 13 years6 years ago

Challenge Numbers

2011: A Prime Year

The year 2011 was quite remarkable, numerically speaking at the very least. Here are some interesting facts about the number 2011.

First and foremost, 2011 is prime. The last prime-numbered year was 2003 and the next will be 2017 (thank you WolframAlpha!).

What is more interesting is that 2011 is a prime that is the sum of eleven consecutive prime numbers! This was first pointed out by @mathematicsprof.

Afterwards, it was pointed out by @republicofmath that 2011 is expressible as another sum of consecutive primes!

When will we see such a numerically interesting year again?

By patrick honner, 13 years4 years ago

Challenge Geometry Teaching

Quadrilateral Challenge — A Solution

Here is one approach to answering the quadrilateral challenge posed earlier. In summary, the challenge was to prove or disprove the following statement: A quadrilateral with a pair of congruent opposite sides and a pair of congruent opposite angles is a parallelogram.

I offer this disproof without words.

By starting with an isosceles triangle, cutting it, rotating one of the pieces, and gluing it back together, we have constructed a quadrilateral with one pair of congruent opposite sides and one pair of congruent opposite angles that it is not necessarily a parallelogram!

By patrick honner, 13 years4 years ago

Application Challenge

The Shape of the Moon’s Orbit

Challenge Resources Teaching

Street Fighting Mathematics

Challenge NYT

Math Quiz: NYT Learning Network

Challenge Numbers

2011: A Prime Year

Challenge Geometry Teaching

Quadrilateral Challenge — A Solution

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