Mathtuition88.com will be the host of the next Carnival of Mathematics! (Submission site: http://www.aperiodical.com/carnival-of-mathematics)
I will now be receiving submissions for Carnival 115.
Firstly, let’s have a discussion on what is so special about the number 115. David Brooks has kindly provided a PDF (Input for Carnival of Math) which the following information is sourced from.
The “Mathematical Association of America” (http://maanumberaday.blogspot.com/2009/11/115.html) notes that:
115 = 5 x 23.
115 = 23 x (2 + 3).
115 has a unique representation as a sum of three squares: 32 + 52 + 92 = 115.
115 is the smallest three-digit integer, abc, such that (abc)/(a*b*c) is prime: 115/5 = 23.
STS-115 was a space shuttle mission to the International Space Station flown by the space shuttle Atlantis on Sept. 9, 2006.
Some other interesting Trivia about 115 include:
115 is the emergency telephone number when calling in Iran. 🙂
115 is the number of cardinals who actually participated to vote for the 265th Pope succeeding the Pope John Paul II in April 2005, even though 117 cardinals were eligible.
Featured posts:
1) How Many Colored Tetrominoes?
Permalink URL:
http://mrburkemath.blogspot.com/2014/09/how-many-colored-tetrominoes.html
Title of post:
How Many Colored Tetrominoes?
Post Author:
Christopher J. Burke
This is a very interesting link about tetrominoes! If you are not sure what are tetrominoes, it is perfectly ok! Just go to the website link above and you will find out!
Question: How many different colored tetrominoes are there if we allow only four colors total?
Second question: What the heck is a tetromino?
Dominoes are a great game with rectangle tiles, composed of two adjacent squares with certain numbers of pips on them. A tetromino is a group of four adjacent squares, each sharing at least one side with at least one other square. In other words, those little falling shapes made popular in the game Tetris, and all of its knock-off variations, as seen below:
2) Using expected frequencies when teaching probability
Summary: The use of the term ‘expected frequencies’ is novel and not widely known in mathematics education. The basic idea is very simple: instead of saying “the probability of X is 0.20 (or 20%)”, we would say “out of 100 situations like this, we would expect X to occur 20 times”.
To learn about this more intuitive and novel way of using expected frequencies to teach probability, visit the site at http://understandinguncertainty.org/using-expected-frequencies-when-teaching-probability.
3) Kettle and Cake Logic
Sigmund Freud tells the tale of a man accused of breaking his neighbour’s kettle. He mounts a three-stranded defence :
1. “I never borrowed it in the first place!”
2. “And anyway it was already broken when I did!”
3. “In any case, it was fine when I returned it!”
Freud used this as an example of the inconsistent logic of dreamland, although you won’t have to look too far afield in the waking world to find examples of similar reasoning[1].
Sounds interesting? View it at: https://plus.google.com/app/basic/stream/z13swvoqnzeyxtbep22fwvqoaxjlefohb04
4) Math Circle – Billiards
From Math Circle: The reason I picked billiards to feature at this particular moment is because twoof this year’s Fields Medalists study billiards: Maryam Mirzakhani and Artur Avila. To find out more about these amazing mathematicians, see our recent Math Munch post.
Visit http://ichoosemath.com/2014/09/14/math-circle-billiards/ to learn more!
5) The curious reluctance to define prime probability logically
The curious reluctance to define prime probability logically. The title says it all, except stress the point that we need to encourage more reasoning from first principles based on what we individually accept as self-evident, and not on what others believe to be self-evident.
6) Hailstone numbers shape a poem
By JoAnne Growney: One of my favorite mathy poets is Halifax mathematician Robert Dawson — his work is complex and inventive, and fun to puzzle over. Dawson’s webpage at St Mary’s University lists his mathematical activity; his poetry and fiction are available in several issues of the Journal of Humanistic Mathematics and in several postings for this blog (15 April 2012, 30 November 2013, 2 March 2014) and in various other locations findable by Google.
Can a poem be written by following a formula? Despite the tendency of most of us to say NO to this question we also may admit to the fact that a formula applied to words can lead to arrangements and thoughts not possible for us who write from our own learning and experiences. How else to be REALLY NEW but to try a new method? Set a chimpanzee at a typewriter or apply a mathematical formula.
Below we offer Dawson’s “Hailstone” and follow it with his explanation of how mathematics shaped the poem from its origin as a “found passage” from the beginning of Dickens’ Great Expectations.
Read more at: http://poetrywithmathematics.blogspot.co.uk/2014/09/hailstone-numbers-shape-poem.html?m=1
7) Approximating e using the digits 1–9
Read this article to learn how to approximate e using just the digitis 1-9! ((1 + 9^{–4^{7×6}})^{3^{2^{85}}}. ) Learn how it works and how remarkably accurate it is! The post is written by Richard Green.
Another closely related post is http://www.flyingcoloursmaths.co.uk/estimating-e/ by Flying Colours Maths Blog!
8）Sand Hill-bert Curve
What is this about? It is a sand model of the Hilbert Curve, or Hilbert space-filling curve!
Check out http://blog.andreahawksley.com/sand-hill-bert-curve/ to learn more.
9) Decending powers of x
I was in one of my colleagues lessons this week.and he was teaching the class to expand quadratic brackets. As the lesson went on he noticed that a number of pupils had been writing the X squared term, then the constant term then the X term so he pulled the class together to tell them that conventionally we write quadratic equations in decending powers of x. This is excellent practice and something we all should be encouraging, but it made me think “Why decending powers of x?”
Interesting question to ponder!
Read more at: http://cavmaths.wordpress.com/2014/09/26/decending-powers-of-x/
10) Extrapolation Gone Wrong: the Case of the Fermat Primes
Read more at: http://blogs.scientificamerican.com/roots-of-unity/2014/09/26/extrapolation-gone-wrong-the-case-of-the-fermat-primes/
11) Erica Klarreich Profiles an Award-Winning Mathematician
Erica Klarreich interviews a famous recent Fields Medallist Stanford University professor Maryam Mirzakhani at: http://www.theopennotebook.com/2014/09/30/erica-klarreich-profiles-an-award-winning-mathematician/
12) Will Rogers phenomenon
Check out the interesting Will Rogers phenomenon, with application to managing a football team! (http://mathsball.blogspot.com.es/2014/09/impossible-transfer-will-rogers-phenomenon.html)
Featured book:
Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail
From a well-known actress, math genius and popular contestant on “Dancing With The Stars”—a groundbreaking guide to mathematics for middle school girls, their parents, and educators
will be larger than any polynomial function, say 
. For example, when x=700, 
, while 
.
by Rudin. It is simply too difficult for beginners or even intermediate students. Any book by 
is also not suitable for beginners, for instance.
by Apostol! Many online sources have very positive reviews on Apostol’s Analysis book. I have read it and found it much more readable than Rudin.
, which is pretty limited if you are doing programming with large numbers (for example over a trillion). For instance, the seventh Fermat number is already 18446744073709551617. I was using Java personally until recently I needed to program larger integers to test out some hypothesis.
which gives the area of a simple polygon whose vertices lie on points with integer coordinates. Surprisingly, it is a relatively modern theorem, the result was first described by 
. We can also see that it is the sum of two triangles 
.
and 
, where 
, express 
in terms of 
.
.
.
. Prove that
Mathtuition88 
