CircleCount helps you better understand Google+

2013-05-13 17:33:45 (0 comments, 0 reshares, 1 +1s)

2013-05-13 17:32:51 (0 comments, 0 reshares, 1 +1s)

Morley Theorem: The trisectors of any triangle's three angles describe an equiangular triangle.

2013-05-13 17:29:51 (0 comments, 0 reshares, 1 +1s)

2013-05-13 13:46:32 (0 comments, 0 reshares, 0 +1s)

2013-05-13 13:42:39 (0 comments, 0 reshares, 0 +1s)

The state of ABC conjecture (pretty bleak)
Also via +David Roberts - claim of proof of weaker case of twin prime  - bounded prime conjecture
https://plus.google.com/103404025783539237119/posts/T5vXKd1N819

2013-05-13 13:39:35 (0 comments, 1 reshares, 1 +1s)

"Though it seems as though the top row of diamonds is darker than the bottom, all the diamonds are actually identical. The sliding diamond seems to get darker as it ascends, but is in fact unchanging."

Source: http://blog.matthen.com/post/50261491742/though-it-seems-as-though-the-top-row-of-diamonds

2013-04-09 13:53:07 (0 comments, 0 reshares, 0 +1s)

It's official

2013-04-09 13:49:30 (1 comments, 0 reshares, 2 +1s)

Check out:

http://mathematics.jds.com/routines.jsp?routine=27

It shows unlimited number of completely worked out examples of polynomial long division.

Change the level from 1 to 5 to see complex ones.

2013-04-09 13:48:20 (1 comments, 0 reshares, 6 +1s)

I did not know you could actually win Snake.

Wowsers.

2013-04-04 13:34:16 (0 comments, 0 reshares, 0 +1s)

I think this is a neat little question!
Share it with your student friends. Enjoy!

2013-04-04 13:31:58 (0 comments, 0 reshares, 1 +1s)

Love this problem.

2013-04-02 21:01:16 (0 comments, 0 reshares, 2 +1s)

Had fun doing some Edexcel S1 mind maps on the paper app with a stylus. Sorry Mr Jobs but its so,much easier than using my finger!

2013-03-28 12:51:09 (0 comments, 0 reshares, 2 +1s)

Wonder: That little intersection of Art and Science.

The artist who created this used to have a blog at: http://desertstars.wordpress.com/design/the-overlap/
Originally posted on this (now dead) tumbler link: http://desertstars.tumblr.com

2013-03-26 16:36:54 (0 comments, 0 reshares, 1 +1s)

2013-03-26 16:36:23 (0 comments, 0 reshares, 1 +1s)

This should be easy now!
;-)

2013-02-28 15:24:30 (0 comments, 1 reshares, 3 +1s)

A significant recent development has been the growth in visual mathematics. The beauty of mathematics is no longer confined to our mind; you can point to it and share it with those who cannot imagine it.
Mathematics with Flair!

2013-02-25 18:56:43 (0 comments, 1 reshares, 1 +1s)

mathematics around the world

99 * 99 =   98 01
1 + 1     ->   2
1 * 1     ->         1

hm , I have to think about it ..... ;-)

goo.gl/ouETw

2013-02-25 18:55:41 (0 comments, 0 reshares, 0 +1s)

Here's an awesomely simple and elegant theorem from complex analysis that helps illuminate some geometric properties of (complex) derivatives:

Marden's theorem – Suppose the zeroes z1, z2, and z3 of a third-degree polynomial p(z) are non-collinear. There is a unique ellipse inscribed in the triangle with vertices z1, z2, z3 and tangent to the sides at their midpoints: the Steiner inellipse. The foci of that ellipse are the zeroes of the derivative p'(z).
http://en.wikipedia.org/wiki/Marden%27s_theorem
http://mathdl.maa.org/images/upload_library/22/Ford/Kalman.pdf

It's great to encounter a theorem like this that can be grasped so immediately and visually, with obvious harmony with many other related strands of knowledge.

Furthermore: Another generalization (Parish (2006)) is to n-gons: some n-gons have an interior ellipse that is tangent toe... more »

2013-02-18 17:57:52 (0 comments, 0 reshares, 1 +1s)

Scattering Amplitudes and the Positive Grassmannian
Nima Arkani-Hamed et. al. have finally released their long-awaited paper, a monumental work from what I've seen so far. It goes farther than ever before to reconstruct scattering processes from geometric primitives in the cleanest way. The main building blocks are just permutations, depicted by a diagram like this one.
http://arxiv.org/abs/1212.5605

A lof of the material here was discussed by NAH in his talk I posted before: <http://bit.ly/10jz4OE> With this new paper there are many aspects that have been greatly clarified.

The traditional formulation of quantum field theory — encoded in its very name — is built on the two pillars of locality and unitarity. The standard apparatus of Lagrangians and path integrals allows us to make these two fundamental principles manifest. This approach, however,requ... more »

2013-02-15 18:28:17 (0 comments, 0 reshares, 1 +1s)

2013-02-15 18:27:55 (0 comments, 0 reshares, 0 +1s)

2013-02-11 19:48:51 (0 comments, 0 reshares, 1 +1s)

For the lover's of Bach, or Riemannian Geometry, this visualization of the "Crab Canon" is super cool, and synesthetic too. ;-)

J.S. Bach - Crab Canon on a Möbius Strip

2013-02-08 19:10:48 (0 comments, 0 reshares, 1 +1s)

2013-02-06 22:16:35 (0 comments, 0 reshares, 2 +1s)

http://www.utsa.edu/today/2013/02/berriozabal.html

2013-02-04 17:46:12 (0 comments, 1 reshares, 2 +1s)

The smooth motion of rotating circles can be used to build up any repeating curve even one as angular as a digital square wave. Each circle spins at a multiple of a fundamental frequency, and a method called Fourier analysis shows how to pick the radii of the circles to make the picture work. Decomposing signals like this lies at the heart of a lot of signal processing.
http://math.stackexchange.com/questions/1002/fourier-transform-for-dummies

2013-02-04 17:45:31 (0 comments, 0 reshares, 0 +1s)

Super excited for the 6.x Jailbreak! It was easy and took only a few minutes.

2013-01-25 18:11:07 (0 comments, 1 reshares, 1 +1s)

A century ago this week, mathematician Andrey A. Markov delivered a lecture on a computational technique now called the "Markov chain" - http://news.harvard.edu/gazette/story/2013/01/an-idea-that-changed-the-world/ 

#mathematics   #math   #markovchain  

2013-01-14 18:58:15 (0 comments, 1 reshares, 3 +1s)

              From the Moebius strip to the Klein's bottle
#KleinBottle is an amazing compact and closed #surface which cannot be embedded in R^3 without making self-intersections. To see this fact you can try to construct it starting from the #MoebiusStrip and trying to glue its opposite edges to close this surface ... of course this cannot be fulfilled in 3 dimensions without tearing up the Moebius strip!

The animation presented here was build with #scilab , which fits perfectly to show 2D surfaces en 3 dimensions  using mesh and colors. It tries to  visualize how Klein's bottle is obtained from Moebius strip and how self-intersections arise. A slower animation is available in my previous post
https://plus.google.com/118331054304456615935/posts/Z6p6pfSPPU6

 Another amazing fact about the Klein's bottle  : at first theobject was named  ... more »

2013-01-10 19:05:15 (0 comments, 0 reshares, 1 +1s)

2013-01-10 16:34:48 (0 comments, 0 reshares, 2 +1s)

I just strolled through the mathematical art exhibit at the JMM. It was very nice to see the work of +Henry Segerman and +Vladimir Bulatov side by side!

I also really like prints by Daniel Gries.I will look him up later when I have more time.

2013-01-10 14:54:16 (0 comments, 0 reshares, 1 +1s)

2012-12-19 14:02:41 (0 comments, 0 reshares, 1 +1s)

I like this math visualization.

Poke around their site for more goodies: http://chartporn.org/2012/12/18/pythagorean-theorem/

2012-12-19 14:02:23 (0 comments, 0 reshares, 1 +1s)

Why are there just five platonic solids (and what are platonic solids!?)

The solids are the tetrahedron, hexahedron (cube), octahedron, icosahedron and dodecahedron.

2012-12-18 14:21:05 (0 comments, 0 reshares, 3 +1s)

2012-12-11 15:39:10 (0 comments, 0 reshares, 0 +1s)

2012-12-10 19:00:46 (0 comments, 0 reshares, 0 +1s)

The new AISD board is already taking big steps against the charter contract

2012-12-10 16:09:09 (0 comments, 0 reshares, 1 +1s)

This is fun: 3/4=1/4 , non obviousness of paths distribution.

2012-12-07 19:03:07 (0 comments, 1 reshares, 3 +1s)

hahah just don't divide by zero folks.... ;)

2012-12-05 22:33:01 (1 comments, 0 reshares, 1 +1s)

http://arstechnica.com/gadgets/2012/12/portals-physics-engine-rebuilt-in-25kb-on-a-graphing-calculator/

2012-11-30 18:21:22 (0 comments, 0 reshares, 3 +1s)

2012-11-26 14:12:43 (1 comments, 1 reshares, 2 +1s)

My animated zoom in to the Mandelbrot set, produced for the documentary BACH & friends, is closing in on 18,000 views!  It's accompanied by Bach's Contrapunctus IX from The Art of Fugue.  The video is a true audiovisual fractal.  If you have a moment, take a peek...

2012-11-20 22:03:26 (0 comments, 1 reshares, 1 +1s)

I think the result of the paper http://arxiv.org/abs/1211.2025 is a nice one, assuming that it is both new and correct.  It relates the number e with Euler's φ-function, the Möbius function and the golden ratio.

The number e (2.718281828459...) is another number like π: it cannot be expressed as a fraction or as the root of a polynomial with rational number coefficients.  It is the base of natural logarithms and turns up in many places.

Euler's φ-function tells you how many numbers in the list 1, 2, 3, ..., (n-1) have no factors in common with n, apart from 1.  For example, if n is 12, the numbers in the list 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 that have no factors in common with 12 (other than a factor of 1) are 1, 5, 7 and 11.  There are four of these, so φ(12) = 4.  We also define φ(1) = 1.

The Möbius function μ(n) takes the value 1 if n is theproduct of an even... more »

2012-11-20 22:00:52 (0 comments, 0 reshares, 3 +1s)

The lonely runner conjecture is a good example of an open mathematical problem that can be explained easily to a nonspecialist.  Suppose that k runners are running in the same direction around a circular track.  A runner is said to be lonely if none of the other runners are within 1/k of a lap of that runner.  For example, if there are three runners on the track, and one of the runners is at least 1/3 of a lap from all the others, then that runner is said to be "lonely".

Now suppose in addition that the k runners are running at distinct, fixed, integer speeds.  The lonely runner conjecture says that if the runners run for long enough, then at some point, each runner will experience loneliness.  For example, if three runners are running around a track at speeds of exactly 4, 5 and 6 miles per hour, then if they run for long enough, each runner will eventually have theexpe... more »

2012-11-20 21:52:13 (0 comments, 0 reshares, 0 +1s)

2012-11-09 18:44:29 (0 comments, 0 reshares, 0 +1s)

2012-11-09 17:39:48 (0 comments, 0 reshares, 0 +1s)

+Malin Christersson originally shared this post ( goo.gl/PuzWH )

Copying fractals

I had to make an interactive version of the tree fractal I reshared earlier. GeoGebra isn't the best program for generating fractals, but the interactivity is cool.
http://www.malinc.se/math/temporary/Tree.html

(You can open any applet from within GeoGebra. Use File->Open Webpage)

#CopyTheFractalFriday   #tgif    #mathematics  

2012-11-08 14:38:33 (0 comments, 1 reshares, 0 +1s)

Nine Circles of Scientific Hell by Neurosceptic.  

2012-11-08 14:37:37 (0 comments, 0 reshares, 1 +1s)

Recently, Kaplan Test Prep released data from a survey showing how college admissions officers check applicant profiles in order to make admissions decisions. This isn’t a new phenomenon: since 2008, I’ve been answering questions about whether residence life, judicial affairs, and other university departments should monitor their students’ Facebook accounts. Here are some reasons why I think such evaluations of applicant Facebook profiles is unethical:

Discrimination in admissions decisions: There is absolutely no way that admissions officers can evaluate student Facebook profiles fairly. First, there is a lack of resources: admissions offices barely have enough staff to keep the machinery of recruitment and the traditional evaluation process going, let alone devote a staff of 10, 100, or 1,000 people to review the Facebook profiles of all entering students.

Even if admissionsoffic... more »

2012-11-08 14:37:02 (0 comments, 2 reshares, 1 +1s)

2012-11-02 17:08:28 (0 comments, 0 reshares, 0 +1s)

Should universities be automatically admitting the top X% at all?