Category: News Clips

Sphere Packing Solved in Higher Dimensions

I enjoyed reading this bit of mathematical news: https://www.quantamagazine.org/20160330-sphere-packing-solved-in-higher-dimensions/

The opening paragraphs:

In a pair of papers posted online this month, a Ukrainian mathematician has solved two high-dimensional versions of the centuries-old “sphere packing” problem. In dimensions eight and 24 (the latter dimension in collaboration with other researchers), she has proved that two highly symmetrical arrangements pack spheres together in the densest possible way.

Mathematicians have been studying sphere packings since at least 1611, when Johannes Kepler conjectured that the densest way to pack together equal-sized spheres in space is the familiar pyramidal piling of oranges seen in grocery stores. Despite the problem’s seeming simplicity, it was not settled until 1998, when Thomas Hales, now of the University of Pittsburgh, finally proved Kepler’s conjecture in 250 pages of mathematical arguments combined with mammoth computer calculations.

Do’s, Don’ts for Parents to Help Teens Build Math Interest and Success

I really enjoyed reading this article: http://www.usnews.com/education/blogs/high-school-notes/2016/04/11/dos-donts-for-parents-to-help-teens-build-math-interest-and-success

A summary:

  • Don’t project negative feeling toward math onto teens
  • Do talk to teens and teachers about what’s being taught in math class
  • Don’t be too quick to hire a tutor for struggling students
  • Do support students with the right tools

I recommend the whole article and the references therein.

Teens do better in science when they know Einstein and Curie also struggled

From http://qz.com/622749/teens-do-better-in-science-when-they-know-einstein-and-curie-also-struggled/:

The study, published in the Journal of Educational Psychology, divided 402 ninth- and 10th-graders from four New York City public schools in Harlem and the Bronx into three groups. One group read an 800-word excerpt from a scientific textbook on the accomplishments of Albert Einstein, Marie Curie, and Michael Faraday (an English scientist who made discoveries about electromagnetism).

Another group learned about the scientists’ personal struggles, such as the fact that Einstein had to flee Nazi Germany to avoid persecution, or Marie Curie had to study in secret because women were discouraged from academic pursuits at the time. The third group learned about the scientists’ intellectual struggles and how they confronted them.

After six weeks, the two groups who learned about how the scientists struggled significantly improved their science grades and increased their motivation to study science. The lowest performing students showed the greatest gains.

Meanwhile, the students who learned only about the scientists’ achievements performed worse. They believed the scientists were innately gifted—unlike themselves.

Statisticians Found One Thing They Can Agree On: It’s Time To Stop Misusing P-Values

From the excellent article http://fivethirtyeight.com/features/statisticians-found-one-thing-they-can-agree-on-its-time-to-stop-misusing-p-values/

A common misconception among nonstatisticians is that p-values can tell you the probability that a result occurred by chance. This interpretation is dead wrong, but you see it again and again and again and again. The p-value only tells you something about the probability of seeing your results given a particular hypothetical explanation — it cannot tell you the probability that the results are true or whether they’re due to random chance…

Nor can a p-value tell you the size of an effect, the strength of the evidence or the importance of a result. Yet despite all these limitations, p-values are often used as a way to separate true findings from spurious ones, and that creates perverse incentives…

If there’s one takeaway from the ASA statement, it’s that p-values are not badges of truth and p < 0.05 is not a line that separates real results from false ones. They’re simply one piece of a puzzle that should be considered in the context of other evidence.

The article above links to the statement by the American Statistical Association as well as various commentaries by statisticians about the proper use of p-values.

 

10 Secret Trig Functions Your Math Teachers Never Taught You

Students in trigonometry are usually taught about six functions:

\sin \theta, \cos \theta, \tan \theta, \cot \theta, \sec \theta, \csc \theta

I really enjoyed this article about trigonometric functions that were used in previous generations but are no longer taught today, like \hbox{versin} \theta and \hbox{havercosin} \theta:

http://blogs.scientificamerican.com/roots-of-unity/10-secret-trig-functions-your-math-teachers-never-taught-you/

Naturally, Math With Bad Drawings had a unique take on this by adding a few more suggested functions to the list. My favorites:

Not Even Scientists Can Easily Explain P-Values

FiveThirtyEight.com published a very interesting feature: asking some leading scientists at a statistics conference to explain a P-value in simple, nontechnical terms. While they all knew the technical definition of a P-value, they were at a loss as to how to explain this technical notion to a nontechnical audience.

I plan on showing this article (and the embedded video) to my future statistics classes.

Not Even Scientists Can Easily Explain P-values