Another Strange Circle

For the fashion-conscious and number-conscious, we have this stylish silver necklace made from the first hundred of so digits of pi.  If you have any mathemagicians on your holiday shopping list, you’re welcome.  Unfortunately I didn’t have much luck ordering one, as my Japanese is pretty rusty.

I’m actually considering the question “Find a circle whose circumference is pi” for an upcoming exam, just so I could show this as the answer.

Oddly enough, this isn’t even my favorite pi-themed necklace!

 

Economics of Gift-Giving

This is an interesting article about some of the psycho-economical factors involved in gift-giving.

http://goo.gl/YJUQz

Starting with the premise “the best gift is something that someone wants, but would feel guilty buying themselves“, the author explores some interesting ideas, including the pain of paying.

Studies suggest that when consumption is directly connected to payment, the result is a decreased feeling of satisfaction in the mind of the consumer.  Regardless of the satisfaction one might feel consuming a product or service, the act of paying reduces that satisfaction.  Marketers go to great lengths to reduce this pain of paying; the success of credit cards is one example of this principle at work.

The author concludes that gift cards really are the best kinds of gifts:  not only can a person get whatever they want,  the card itself frees the user of the pain of paying, which itself may be the best gift of all.

This reminds me a bit of the curious psycho-economic results associated with pricing models I read about earlier this year.

The Euler Archive

This is a great on-line resource hosted by the Math Department at Dartmouth University:  a comprehensive collection of the works of (and about) Leonhard Euler.

http://www.math.dartmouth.edu/~euler/

Euler, indisputably one of the greatest mathematicians in history, authored over 800 papers in his lifetime, touching on every area of mathematics then in existence.  In addition, Euler made significant contributions to physics, astronomy, and applied sciences as well.

The archive features historical and biographical information, related resources, and digital copies of over 800 original documents.

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!

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