Prove that e is irrational.

Find the connection between the constructed length and the original rectangle.

Find the radius of the circle inscribed inside the isosceles triangle.

Show how the values 1, 2, 4, 8, 16, 32, 64, 128, and 256 can be placed in a 3x3 square grid so that the product of each row, column, and diagonal gives the same value.

Prove that the roots of the polynomial, xⁿ + c_n-1x^n-1 + ... + c₂x² + c₁x + c₀ = 0, are irrational or integer.

Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square.

Prove that π is irrational.

Which fits better... a round plug in a square hole or a square plug in a round hole?

Prove that cos(x) is algebraic if x is a rational multiple of Pi.

Find the side length of the square inscribed inside the right angled triangle.

What fraction of the large red circle do the infinite set of smaller circles represent?

FLU SECURITY [More]

Is it hopeless to try to compute the shortest route to visit a large number of cities? Not just a good route but the guaranteed shortest. The task is the long-standing challenge known as the traveling salesman problem, or TSP for short.

We the People of the United States, in Order to form a more perfect Lifestyle, establish Fairness, ensure blood pressure Tranquility, provide for the common Text Messager, promote less Outrage and secure Cell phone Service that’s anywhere near as good as it is in Other Countries, do ordain and establish this Cellular Bill of Rights.

One of the oldest unsolved problems in mathematics is also among the easiest to grasp. The weak Goldbach conjecture says that you can break up any odd number into the sum of, at most, three prime numbers (num­bers that cannot be evenly divided by any other num­ber except themselves or 1). For example: [More]

An excavation of an archaeological site in Guatemala has uncovered Mayan astronomical records dating to the ninth century A.D. The tabulated numbers, which predate existing Mayan astronomical documents by several hundred years, chart the motion of the moon and also seem to relate to the orbits of Mars and Venus. (And good news: they do not predict the world will end this year --in fact, some of the numbers appear to refer to dates far in the future.)

The shadowy nature of illegal media down­loading makes it difficult for researchers to analyze the true relation between piracy and lost sales. Does every movie download represent a theater ticket left unpurchased, as the movie industry contends? Or are most downloaders people who never would have bought a ticket in the first place?

Earlier this year Iran's defense minister put the world on notice: His nation had developed the ability to "easily" watch spacewalking astronauts from the ground. The announcement was largely ignored, in part because it made the minister sound like a James Bond villain. The boast was also a bit anticlimactic, given that even amateur astronomers are already recording in detail what happens in low Earth orbit. Both the technology involved and the techniques used to observe satellites and even the occasional astronaut perched outside the International Space Station (ISS) are improving, much to the presumed chagrin of governments looking to keep certain on orbital activity confidential. [More]

In his new book, In Pursuit of the Unknown: 17 Equations That Changed the World , Ian Stewart recounts one of the worst jokes in the history of science. You can develop your own setup from first principles once you know the punch line: “The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.” Never mind how Native Americans were in possession of a hippopotamus--the important thing is that the Pythagorean theorem is so well known that comedy writers consider it fair game even if that game couldn’t possibly be found on the correct continent.

Some years ago two nutrition experts went grocery shopping. For a dollar, Adam Drewnow­ski and S. E. Specter could purchase 1,200 calories of potato chips or cookies or just 250 calories worth of carrots. It was merely one example of how an unhealthy diet is cheaper than a healthy one. This price difference did not spring into existence by force of any natural laws but largely because of antiquated agricultural policies. Public money is working at cross-purposes: backing an overabundance of unhealthful calories that are flooding our supermarkets and restaurants, while also battling obesity and the myriad illnesses that go with it. It is time to align our farm policies with our health policies.

Last November, Russia launched a widely anticipated mission to the Martian moon Phobos. The craft would gather samples from the moon’s surface to help determine if future space crews could obtain valuable supplies of oxygen there en route to Mars. For Russia, the mission was supposed to mark a “cavalry charge” that would redeem a quarter-century of interplanetary impotence. Instead it turned into a cosmic humiliation when the craft died shortly after takeoff and fell back to Earth.

Key concepts [More]

As part of my job at RiAus I get asked to write the occasional blog about an upcoming event. I wrote this for an event that occured last week about fractal geometry with the amazing Prof. Michael Barnsley . It was a great event and my blog post was just a little teaser for it.

Stuck on a tricky math problem? Start clapping. Grade school kids who learned about fractions through a rhythm-and-music-based curriculum outperformed their peers in traditional math classes. The work is in Educational Studies in Mathematics . [Susan Joan Courey et al., " Academic music: music instruction to engage third-grade students in learning basic fraction concepts "]

High status confers a rosy worldview, according to research available online last August in Organizational Behavior and Human Decision Processes . Psychologists asked college students to write essays about having more prestige than others or being low on the totem pole, thus priming them to think of themselves as having either high or low status. Then the students were told they could send $10 to an unseen partner; the money would be tripled, and the phantom partner would return as much as he wanted. Forty percent of the high-status group sent the $10 versus 12 percent of the low-status group.

Windswept from cloud to cloud until they flutter to Earth, snowflakes assume a seemingly endless variety of shapes. Some have the perfect symmetry of a six-pointed star, some are hexagons adorned with hollow columns, whereas others resemble needles, prisms or the branches of a Christmas tree.

Key concepts [More]

ENTOMOLOGICAL ETHICS [More]

The number of U.S. undergraduate degrees being awarded in most STEM disciplines (science, technology, engineering and math) has risen steadily in recent years{link to G Sci page}. Yet some American employers say they are having trouble finding candidates to fill STEM jobs. The mismatch is not occurring because of an actual shortage of graduates; the numbers of job openings and new degree holders align fairly closely. And the shortfall is not because more foreign-born students are returning home after earning U.S. degrees, as has been rumored lately.

Reggie Miller, Michael Jordan, Kobe Bryant. They’ve all gone on seemingly memorable shooting streaks. But past research has shown that the so-called hot hand is a myth, rooted in our tendency to see patterns where there are none.

Humankind’s efforts to tell time have helped drive the evolution of our technology and science throughout history. The need to gauge the divisions of the day and night led the ancient Egyptians, Greeks and Romans to create sundials, water clocks and other early chronometric tools. Western Europeans adopted these tech­nologies, but by the 13th century, demand for a dependable timekeeping instrument led medieval artisans to invent the mechanical clock. Although this new device satisfied the requirements of monastic and urban communities, it was too inaccurate and unreliable for scientific application until the pendulum was employed to govern its operation. The precision timekeepers that were subsequently developed resolved the critical problem of finding a ship’s position at sea and went on to play key roles in the industrial revolution and the advance of Western civilization.