I have always been fascinated with menus, and one of my favorite pastimes is analyzing menus for price discrepancies.
For example, how many different prices can you spot Wendy’s charging here for the same Meal Combo upgrade?
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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:
http://learning.blogs.nytimes.com/2011/02/14/test-yourself-math-feb-14-2011/
This problem is based on comparing the total national incomes of the United States and China. My solution offers a simple way to turn per capita income and population into meaningful percentages.
Challenge Geometry
Geomagic Squares
The magic square is an ancient and well-known mathematical object. In the figure at the right, the sum of every row, column, and diagonal is the same, namely, 30. This is a basic magic square.
Magic squares have been around for thousands of years, and there many variations have been explored. Which makes the invention of a new kind of magic square all the more amazing: the geomagic square.
http://www.newscientist.com/gallery/magical-mathematics/2
These geomagic squares turn the algebraic magic square into something geometrical: instead of numbers summing up to the magic constant in every direction, polygonal tiles can be put together to form the same shape in every direction! Here’s an example.
With some flipping and rotating, every sequence of tiles in this “square” can be arranged to make the same figure, namely, a 4 x 4 square with one small square missing. The example at the right shows the middle row being assembled to form the “magic constant”: the white square in the middle is the missing square.
The natural questions: how do you construct geomagic squares? Can you make a geomagic square for any given “magic constant”? For a given “magic constant”, how many geomagic squares can you create? What others can you think of?
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:
http://learning.blogs.nytimes.com/2011/02/2/test-yourself-math-feb-2-2011/
This problem involves estimating the per-person health care expenditures in the United States.
Application Challenge
Piggy Bank Estimations
Here are some interesting results regarding the recent Piggy Bank challenge.
Below are two graphs representing reader estimates. The graph on the left (Part 1) shows reader estimates without knoweldge of the weight of the Piggy Bank. The graph on the right (Part 2) shows reader estimates with knowledge of the weight.
The red bars represent the actual value of the Piggy Bank: $80.41. Not only are there significantly more “close” estimates in Part 2, the average estimate is $70.02; this is about 13% less than the actual value. Compare that with the average estimate in Part 1 of $46.98, which is about 41% less than the actual value.
Did readers actually use the knowledge of the weights to make a better “guesstimation”? Or is this perhaps an example of the anchoring effect?
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