Math and Multimedia Blog Carnival #12

Welcome to the 12th edition of Math and Multimedia blog carnival. Yes, you get a dozen posts this time.  Before we do that let’s look at some trivia about the number 12.

The number 12 is strongly associated with the heavens – 12 months, the 12 signs of the zodiac, the 12 stations of the Sun and the Moon. The ancients recognized 12 main northern stars and 12 main southern stars. There are 24=12×2 hours in the day, of which 12 are in daytime and 12 in nighttime.

In mathematics, twelve as we all know is a composite number and the smallest number with exactly six divisors, its proper divisors being 1, 2, 3, 4, 6 and 12. Twelve is also a highly composite number, the next one being24. It is the first composite number of the form p²q; a square-prime, and also the first member of the (p²) family in this form. 12 has an aliquot sum of 16 (133% in abundance).

Accordingly, 12 is the first abundant number (in fact a superabundantnumber) and demonstrates an 8 member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3-aliquot tree. The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20).

Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of 12’s proper divisors that add up to 12 (all of them but with 4 excluded), 12 is a semiperfect number. If an odd perfect number is of the form 12k + 1, it has at least twelve distinct prime factors.

Twelve is a superfactorial, being the product of the first three factorials. Twelve being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.

Twelve is the ninth Perrin number, preceded in the sequence by 5, 7, 10, and also appears in the Padovan sequence, preceded by the terms 5, 7, 9 (it is the sum of the first two of these). It is the fourth Pell number, preceded in the sequence by 2 and 5 (it is the sum of the former plus twice the latter). Thanks to Wikipedia for these.

Now, let’s go to the shared articles and some of my finds.

Guillermo Bautista, the blogger who started this Math and Multimedia Carnival presents Why Finger Multiplication Works | Mathematics and Multimedia which he posted at Mathematics and Multimedia. KathyHS87 shares why she loves Futurama in The Futurama Theorem (Or Why I Love Futurama) posted at Life As I Know It. I guess you have to click the link to know what Futurama is. Continuing the ‘why’ questions here’s my two posts about What is algebra? Why study it? and my popular post about Trigonometry – Why study triangles? in Mathematics for Teaching.

And just in case you are wondering about segments with  irrationals lengths, check Sanjay Gulati’s Math Academy which presents a GeoGebra applet showing the position irrational numbers in the numberline and John Golden’s presents Spirograph 1 also with GeoGebra applet posted at Math Hombre . And while we are on the subject of technology, check out David R. Wetzel 12 Free Mobile Math Apps for the iPod Touch posted at Teaching Science and Math and

Will Emeny shares his find in Real World Maths- Tsunami Investigation Using Google Earth posted at Great Maths Teaching Ideas. Terrance Banks also announces he’s back with blogging with new stuff in Been gone for a while but back with new stuff!! posted at So I Teach Math and Coach?.

Carnival hosted in this blog will not be complete without sharing teaching and learning ideas. David Coffey shares his ideas in What support do learners need? posted at Delta Scape. Denise of Let’s Play Math presents Number Bonds = Better Understanding. And just in case you are forgetting, the first commandment in planning mathematics lesson is to  know about students Mistakes and Misconceptions.

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