144th Carnival of Mathematics
The most obvious thing about 144 is probably that it is a perfect square, ie 12×12=144. But it isn't just any square number, it is in fact the largest one to exist in the Fibonacci series:
The aesthetically pleasing Fibonacci spiral constructed by means of the Golden Ratio
And it's rather eerie current US president Donald Trump possesses a side profile that resembles the same spiral:
A truly sad,sad day for Mathematics to be associated with this particularly vile, obnoxious Homo Sapien? Hmm.
Apart from being a Fibonacci number, 144 is also unofficially recognized as a Harshad number in recreational Mathematics. But what exactly is a Harshad number? Well, a clean definition goes as such: it is an integer (in base 10 format aka the conventional number system) that is divisible by the sum of its digits. In this instance, the sum of the digits constituting 144 = 1+4+4=9, and 144 is completely divisible by 9 as 144 ÷ 9 =16, so there you go.
A third and final fun fact about 144: it is the smallest number whose fifth power is a sum of four (smaller) fifth powers. Discovered in 1966 by L. J. Lander and T. R. Parkin, it is mathematically articulated as such:
Now it's time to get down to serious business of showcasing them works of blogging Maths folks. Welcome to the 144th Carnival of Mathematics.
Manan Shah offers some problems he personally feels teachers should add to their repertoire when teaching the topic on parabolas. He further explained:
"These problems are important, yet are often being overlooked. They are designed to get students thinking a little bit more about the structure of parabolas, quadratics, and the quadratic formula as well as how the study of these objects leads to other areas of Mathematics."
Over at The Maths Mentors, a "Crack My Treasure Chest" game has been fashioned to help students thoroughly explore the Greatest Common Factor (GCF) concept. Educators seeking inspiration for fresh classroom activities may wish to check this one out.
Do you know what Havercosine or Excosecant is? The Scientific American website has Evelyn Lamb serving up a list of 10 trigonometric functions that have, erm, somewhat gone extinct in the present world order of Mathematics, which may or may not have been 'sincerely' motivated by The Onion's outrageous false piece titled "Nation’s Math Teachers Introduce 27 New Trig Functions".
Former engineer turned passionate Mathematics teacher Yana Mohanty received a 360 camera on her birthday approximately 6 months ago, and it dawned on her that it can be used to help people see the transformations that topologists call homeomorphisms- roughly stretching and bending a shape without tearing. Hence her blog post "Bagels, Pretzels... Cubical Frames", which seeks to demonstrate how a cubical frame can be stretched to a pretzel with 5 holes. A side remark in her submission to this edition of the carnival mentioned that the post was inspired by the prominent role topology played in the research of last year's Physics Nobel Prize winners (David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz).
In "Fractivities!", Jennifer Schuetz from the Fractal Foundation helps kids get up close and personal with the mathematical premise of fractals in a fun-filled hands on session; younger kids were seen happily drawing Sierpinski triangles on guided worksheets, while the older ones got to physically construct them using wooden sticks and glitter glue.
As far as pedagogy is concerned, Lucy Rycroft-Smith recommends a series of posts Maths educators can consult at the Cambridge Mathematics portal: "The Unreasonable Man" (a lovely blog about proof, reasoning and the history of Maths), "Mental Imagery" (an incredibly thought-provoking blog about what mental imagery (and other senses) might be and how it can help learners of maths at all levels) and "What's In The Pot? " (about probability and how to teach it using 'urn models', in which the author gently provokes thought about the basic models behind early probability teaching). Denise Gaskins over at Let's Play Math generously dishes out a wholesomely curated buffet of links to various Maths forums, blogs, journals and e-book downloads which will certainly have both parents and teachers feeling most delighted and grateful for.
Jason Merrill endeavors to relate algebraic and pictorial ways of understanding the Pythagorean theorem and the Law of Cosines, which he largely succeeds as evidenced in his "Geometry, Algebra, and Intuition" piece. He expands upon the rationale for doing so, stating that such an attempt "shows a lesser-used way of visualizing the dot-product that makes its main properties (bilinearity, symmetry, relationship to squared length) clearer than the "scaled projection" picture."
Finally, meet Tony. He is a Mathematics lecturer at a University in London who rides on public buses daily, and he recently contemplated the implementation of a possibly more efficient transport solution by means of employing number theory. Talk about making really good use of time even when one is on the move.
And things draw to a close once more in this edition. It is humbly hoped you will have as much fun reading the content showcased as I did assembling it all together. The upcoming 145th Carnival of Mathematics will be hosted at the Aperiodical blog, so stay tuned.
(PS: I would like to accord a sincere thank-you to Katie Steckles for giving me the opportunity to contribute to this blossoming math blogging community. )
2 April 2017