## Tuesday, October 28, 2014

### Happy 20^2 (400th Blog Post)

Hello everyone,

This is the 400th blog entry.  I want to thank everyone who follows my blog, reads, and comments on my blog.  You rock!

For today’s blog entry, here are some mathematical, and fun facts regarding the number 400.

Mathematical Facts:

20^2 = 400

The divisors of 400 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400.  The sum of these divisors is 961.

The prime factorization of 400:  400 = 2^4 * 5^2

400 is a composite number.  The nearest primes to 400 are 397 and 401.

Totient function:  ϕ(400) = 160.  That is, there are 160 positive integers less than 400 that are coprime to 400.  That is, the GCD of 400 and such coprime numbers is 1.

A square matrix of 400 x 400 has 160,000 elements.

A gradian (also symbolized as gon) is an angle measure, splitting a circle in 400 angular units.  The gradian is primarily used in civil engineering and surveying in Europe.

180° = π radians = 200 gon

Computing and Calculator Facts:

The Hewlett Packard HP 12C Platinum Edition finance calculator has a programmable memory of 400 steps.

Atari released the Atari 400 computer in late 1979.  It was an entry-level computer.  Specifications include:  1.8 MHz processor, 8K RAM (expandable to 48K), and uses a TV screen a monitor.  Resolution of the computer varies, 320 x 192 monochrome to 160 x 96 color screen.  The Atari 400 used cartridges to run programs and games.

A YouTube Video on the Atari 400, one of many:  https://www.youtube.com/watch?v=UNf8OQaud2M

Science Facts:

Visible light that has a wavelength of 400 nm (nanometers) has the color of violet.

On average, the average distance from the Sun to Earth is about 400 times the average distance from the Moon to Earth.     (http://space-facts.com/solar-eclipse/)

A person who has lived 400 days is of age 1 year, and a little more than 1 month.

Rules of the Gregorian Calendar:  Most century years, 1900 and 2100 for example, are not leap years.  However, century years that are divisible by 400, such as 1600, 2000, and 2400, are leap years. (http://www.timeanddate.com/date/leapyear.html)

Games:

If you went around the entire board on a Monopoly game 10 times, you would traveled 400 spaces.

The card game 400, originated in Lebanon, is a trick taking game between two teams of two players.  In 400, players individually make bids to how many tricks they can win.  Hearts is the trump suit.

If you want to play online: http://www.400cards.com/index.php

Business and Entertainment Facts:

This will probably make you jealous, inspired, or maybe both:  Forbes Magazine keeps track of the richest 400 individuals in the United States.  In 2014, the net worth of the Forbes 400 is a combined \$2.29 trillion.  (http://www.forbes.com/forbes-400/)

The Barron's 400 index is an index of 400 top stocks.  (http://online.barrons.com/public/page/barrons_400.html)

The Brickyard 400 is an annual NASCAR race in Indianapolis, Indiana.  The race is 400 miles, or about 643.739 km.  (http://en.wikipedia.org/wiki/Brickyard_400http://www.indianapolismotorspeedway.com/events/brickyard)

The Walking Dead: The First Season video game by Telltale had a downloadable episode titled “400 Days”, designed as an episode bridge between seasons 1 and 2.  (http://walkingdead.wikia.com/wiki/400_Days)

There is a German music electronic artist named Kenkraft 400.  Chances are if you been to a recent sports event, you have heard “Zombie Nation”.

Happy 20^2!

Eddie

This blog entry is property of Edward Shore.  2014

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