Year: 2011

Google’s 2-step verification: An excellent added security

Miscellaneous, Off Topic

A week ago, I enrolled in Google Account’s 2-step verification, and I think it’s a very good security improvement. The 2-step verification protects users from password compromise and identity theft.

If you enroll in Google’s 2-step verification, you will be asked to enter your mobile number. Each time you login to a computer, you are required to enter a verification code sent to your phone. That means, that if somebody wants to steal or hack your account, he must have your login name, your password,  and your phone too! You can also have a back-up mobile number which will be used in case you lost your mobile phone. To save you the trouble of entering a code every login, you may allow Google to remember your computer for 30 days.

Google also  allows you to print verification codes, each of which can be used once, in case you don’t have access to both mobile phones.  Once you run out of codes, you can login to your account and generate more.

For more information about the 2-step verification, click here.

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Guest Post: GeoGebra Investigation of the Equiangular Spiral in the Flight of an Insect

College Mathematics, Math in Real Life

If you are near an outside lamp after dark you will notice some insects spiraling around it. Are they simply attracted to the light?

If an insect positions its body in a certain direction and keeps a constant angle with the light rays coming from the Sun or the Moon (which are parallel), it will follow a straight line trajectory. However, people brought to the night sky electric lights emitting radial rays. The insects, continuing to follow the same way of orientation will keep a constant angle with the light rays, but this time they will not fly on a straight line. The trajectory will be an equiangular spiral.

Here are two GeoGebra applets modeling this phenomenon.

http://lima.osu.edu/people/iboyadzhiev/GeoGebra/FlightOfInsect.html

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Irina Boyadzhiev (author) is a lecturer in mathematics at the Ohio State University at Lima. Her GeoGebra applets are available at: 

http://lima.osu.edu/people/iboyadzhiev/MyGeogebra.htm

 

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Divisibility by 3

High School Mathematics

This is post is the fourth part of the Divisibility Rules Series.  The first three posts are about divisibility by 2, divisibility by 4 and divisibility by 5 and 10. In this post, we discuss divisibility by 3.

When we divide things, we split them into ‘groups.’ Of course, we cannot always divide them equally.  For example, dividing 13 balls by 3 is the same as putting the balls into containers in groups of three. In dividing 13 by 3, 1 is left out as shown below. We have learned that the excess or the ones that are left out during division are called remainders. In the figure below, we can say that 13 divided by 3 gives a remainder of 1.

 

Divisibility by 3 is not as easy as divisibility by 2, by 5 or by 10. However, we note the following observations when we divide by 3. » Read more

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