Carnival of Mathematics #105

Yay! It’s Carnival of Mathematics #105.

The Carnival of Mathematics is a monthly roundup of Mathematics blogging from around the world. I’m Über excited that I will be hosting it. This month, I have amazing submissions from Mathematics Theorems to Multiplication Tricks.

Photo Credit – Yu-Gi-Oh!

Since the Carnival of Mathematics will be in Africa this month, I might as well share a native fact about 105. In Amharic, an Ethiopian Language, 105 is written as:

፻፭

Number Gossip says it’s the smallest number such that the 105th cyclotomic polynomial has a coefficient that differs from 0, 1, or -1. Okay. I also found this property on What’s Special About This Number?: 105 is the largest number, $n$ , with the property that $n - 2^k$ is prime for $k > 1$ . Number Gossip also gives some other not-so-unique properties of 105 – It’ s deficient, lucky and composite which I think are really odd. The Online Encyclopedia of Integer Sequences says that 105 belongs to the sequence of numbers formed from the product of 3 consecutive primes. One more: 105 occurs 200062 times in the first 200 million digits of $\pi$ . Cool, right?

Back to business.

Here’s what hot this month in the world of mathematics blogging:

Education

Photo Credit – MYP @ Global Jaya International School

In Moving Towards more Meaningful Assessment in 21st Century Mathematics, Dan Pearcy says:

I want my students to understand that the concepts behind why things work are more interesting, creative and important than simply being able to use things with little understanding. One way to ensure they realise this is if my assessments reflect it. The post includes an example assessment for Grade 6 (Year 7) Shape which I would appreciate feedback on for improvement.

Matthew Jones’ post, Engage!, explains a fun way of actively engaging a class through collaboration while Sarah Hagan shares her childhood experiences and her motivation behind sticking to teaching in Why I Teach.

Paul Karafiol also reflects on his life as a teacher and the impact his students have had on him. In Reflection before Report Cards, Matt explains his strategy of getting his students to reflect in Mathematics Class to help them take control of their learning. Colleen Young gets us into the festive mood with Christmas 2013.

Patrick Honner has this to say about When Desmos Fails:

Here I explore an anomaly in how Desmos, a free online graphing calculator, handles a removable discontinuity. Some great discussion ensued!

Mathematics in the Real World

Photo Credit – The Olami-Feder-Christensen Model of Earthquakes

Michael J. Grayling gives a thoughtful review of John Adam’s highly entertaining and accessible book, X and the City: Modeling Aspects of Urban Life.

In The life and numbers of Fibonacci, Ron Knott and the Plus team provide the interesting history of the Fibonacci sequence while presenting interesting occurrences of this famous sequence in nature.

Ev elyn Lamb describes How the Simpsons (And You) Can Multiply by Seven Using Your Fingers. (I impressed a couple of friends with the trick). MarkCC uses the Birthday Paradox to explain how our intuition might not always produce the best of guesses.

Peter Rowlett discusses induction, deduction, maths, science and even Sherlock Holmes in his exciting Why maths isn’t like science (and may be evil) while Ivars Peterson explores the mathematics behind a variant of a card trick in Counting on Success.

Matifutbol has this to say about The Amazing Case of the Extra Car:

What do you know about Alabama Paradox?

Let’s have a look at the new Matifutbol story, and try to solve it! The sponsor of the Football World Championship 2015 in Canada is going to give away some gifts to the best scorers. But a last minute change in the number of gifts creates a curious change in their apportionment.

Exciting Geometry

Photo Credit – Math Education Page

Ev elyn Lamb describes John Baez’s Rolling hypocycloids:

This was a great post about the different ways hypocycloids can roll in hypocycloids with different numbers of cusps. It includes some interesting links to physics as a nice little bonus.

Ev elyn also has this to say about A Cuddly, Crocheted Klein Quartic Curve where she explains the really cool geometry behind the Klein Quartic:

I wrote this post about a cool new thing Daina Taimina made: a representation of the Klein quartic curve using crochet.

Kalagz shares interesting facts and proofs behind Ceva’s Theorem and Oluwasanya finds Mathematics in Stanford.

Applications

Photo Credit – Mars Will Send No More

Simon Gladman talks about Mutually Catalytic Binary Gray Scott System saying:

Here’s an alternative method of coupling reaction diffusion models: all my previous experiments with coupling have involved essentially adding the u and v output values into one model from another. However this version involves using the the same u and v values from one model to affect the parameter values in another. The results show some really nice coupling phenomena. My favourite examples have one system creating a coral like labyrinth with the other system creating mitosing solitons and the coupling binding the solitons to the coral structure .

Fun and Humour

Photo Credit – Zen of Zero

In A Little Bit of Statistics Is a Dangerous Thing, Shecky Riemann takes another ‘jab’ at statistics with a joke he finds in Simon Singh’s The Simpsons and Their Mathematical Secrets.

Robert Kaplinsky presents a silly question to bunch of 8th grade kids and lets us enjoy the interesting results in How Old Is The Shepherd? Oluwasanya goes creative with his video on the Meaning of Olympiads.

Mathematicians and Sporting Events, by the Calculus Humor Team, shows why Mathematicians are no longer allowed to sporting events while JoAnne Growney shares a cute Mathematical poem about nature in Algebra cadabra.

Finally, Ben Orlin concludes the Carnival with Headlines from a Mathematically Literate World.

Ladies and Gentlemen, this is it from CoM #105! Thanks to those who sent in their submissions.

Photo Credit – Geek Wisdom

Check out Shecky Riemann’s Math-Frolic for the previous Carnival and watch out for Carnival of Mathematics #106 on the Ap eriodical. O da abọ (That’s Yorùbá for good bye) :).