New mathematics artwork from Hamid Naderi Yeganeh.
This fractal is constructed by an Africa-like octagon and its lateral inversion.:
The height of the biggest octagon is φ times longer than the height of second octagon; where φ is the golden ratio. (see the following image) It is a necessary and sufficient condition to see the white triangles in this fractal.
A post on Farnam Street. A quote:
Feynman knew the difference between knowing the name of something and knowing something. And was often prone to telling the emperor they had no clothes as this illuminating example from James Gleick’s book Genius: The Life and Science of Richard Feynman shows.
Educating his children gave him pause as to how the elements of teaching should be employed. By the time his son Carl was four, Feynman was “actively lobbying against a first-grade science book proposed for California schools.”
It began with pictures of a mechanical wind-up dog, a real dog, and a motorcycle, and for each the same question: “What makes it move?” The proposed answer—“ Energy makes it move”— enraged him.
That was tautology, he argued—empty definition. Feynman, having made a career of understanding the deep abstractions of energy, said it would be better to begin a science course by taking apart a toy dog, revealing the cleverness of the gears and ratchets. To tell a first-grader that “energy makes it move” would be no more helpful, he said, than saying “God makes it move” or “moveability makes it move.”
Read the full story.
A new paper in The De Morgan Gazette:
Form the Introduction:
This paper is a text of a talk at the opening of the Exhibition Sublime Symmetry: The Mathematics behind De Morgan’s Ceramic Designs in the delighful Towneley Hall Burnley, on 5 March 2016. The Exhibition is the first one in Sublime Symmetry Tour organised by The De Morgan Foundation.
I use this opportunity to bring Sublime Symmetry Tour to the attention of the British mathematics community, and list Tour venues:
06 March to 05 June 2016 at Towneley Hall, Burnley
11 June to 04 September 2016 at Cannon Hall, Barnsley
10 September to 04 December 2016 at Torre Abbey, Torbay
10 December 2016 to 04 March 2017 at the New Walk Gallery, Leicester
12 March to 03 September 2017 at the William Morris Gallery, Walthamstow
William De Morgan, Peacock Dish. The De Morgan Foundation.
MathsBombe – the new maths-based competition aimed at A-level students (but open to all UK students in Year 13 (or equivalent) or below) – started this afternoon. This is the sister competition to the now well-established `Alan Turing Cryptography Competition’ but aimed at an older group of students and featuring mathematical puzzles. If you know anybody who would be interested in this then please pass this on (or if you know of any way of promoting the competition that we haven’t thought of then please let us know!). The url is: www.maths.manchester.ac.uk/mathsbombe
From Richard Rusczyk:
Over the last decade, many students have asked us how to get involved in research. To address this need, we are partnering with MIT PRIMES, which has trained many outstanding high school student researchers over the last several years. MIT PRIMES/AoPS CrowdMath will allow mathematically sophisticated high school students to collaborate on unsolved problems under the mentorship of outstanding mathematicians. CrowdMath begins with a series of Resources for students to discuss over the next couple of months. On March 1, we will release the official research problems, which will be based on material students learn while discussing the Resources.
Our goal is to discover new knowledge! Should we succeed, we’ll produce a research paper based on our collective work.
Visit the MIT PRIMES/AoPS CrowdMath pages for more details.
From a brilliant blog by Allen Downey:
The inspection paradox is a common source of confusion, an occasional source of error, and an opportunity for clever experimental design. Most people are unaware of it, but like the cue marks that appear in movies to signal reel changes, once you notice it, you can’t stop seeing it.
A common example is the apparent paradox of class sizes. Suppose you ask college students how big their classes are and average the responses. The result might be 56. But if you ask the school for the average class size, they might say 31. It sounds like someone is lying, but they could both be right.
The problem is that when you survey students, you oversample large classes. If are 10 students in a class, you have 10 chances to sample that class. If there are 100 students, you have 100 chances. In general, if the class size is x, it will be overrepresented in the sample by a factor of x.
That’s not necessarily a mistake. If you want to quantify student experience, the average across students might be a more meaningful statistic than the average across classes. But you have to be clear about what you are measuring and how you report it.
This Geobebra applet follows a theorem by Ludolph van Ceulen from 16th century:
A drawing from a book by Ludolph van Ceulen (1540 – 1610) book,
Our American colleagues celebrate today Pi Day, although, technically speaking, it is American Pi Day: for the rest of the world, today is 14/03/14. A brilliant article by Steven Strogartz in The New Yorker, a brief quote:
What distinguishes pi from all other numbers is its connection to cycles. For those of us interested in the applications of mathematics to the real world, this makes pi indispensable. Whenever we think about rhythms—processes that repeat periodically, with a fixed tempo, like a pulsing heart or a planet orbiting the sun—we inevitably encounter pi. There it is in the formula for a Fourier series: […]
Read the whole article.
University Mathematics in Perspective
What’s so special about multiplication? To begin with, it is universal and therefore unavoidable. We all had to learn it. And our children will have to learn it too, in some shape or form. Here’s something else – the way you will help your children learn multiplication will mirror the way you learned it yourself, unless you take steps to change that. So how did you learn?
Did you spend hours repeating “the facts” with chants, flashcards, and seemingly endless drills? A lot of things have changed since we were children. There must be more effective ways of mastering multiplication! And there must be ways to make it relevant to our lives!
Let’s dig deeper. Do you remember how you felt studying the multiplication tables? For so many people we meet, the dislike and fear of math can be traced all the way back to their struggles to understand (and not just memorize) multiplication. Can we change this pattern so our children, approaching multiplication, feel not fear but curiosity, not anxiety but joy, not alienation but affinity? Can multiplication be more about smart play, rich mathematical thinking and usefulness everywhere in life?
This is what our Multiplication Explorers course is all about. It explores holistic approach to learning multiplication. Memorization based on smart number patterns is a part of it. The course also includes bridges between multiplication and natural world, as well as links to many virtual and imaginary worlds in books, music, technology, art, and games.
We invite you to boldly go beyond the familiar representations of multiplication such as skip counting and repeated addition, to explore many more meaningful, beautiful, and fun models. This course is a launch pad to adventures across the universe of multiplication.