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Your steps should be in a cycle: short, long, long. Long in this case means a double step. Thus, you will cover five stairs in one short-long-long cycle. In addition, you should always start the first cycle on the same foot. Suppose you start on the left foot, then after two cycles you are back on the left foot…
"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook…
The idea of a canon is that one single theme is played against itself. This is done by having "copies" of the theme played by the various participating voices. But there are means' ways to do this. The most straightforward of all canons is the round, such as "Three Blind Mice", "Row, Row, Row Your Boat", or " Frere…
...basic Roman arithmetic is largely rather simple, even for those of us spoiled by Arabic notation. Addition is no sweat, because complex Roman numbers already use what math pros call additive notation, with numerals set beside one another to create a larger number. VI is just V plus I, after all. To add large…
Most real-world numbers aren’t always so nice and neat, with wholenumber multiples. If, say, Plant A grew from 2 to 3 feet, and Plant B grew from 6 to 8 feet, then we would say that Plant A grew 1/2 of its original height, whereas Plant B only grew 1/3 of its original height. Such reasoning exemplifies multiplicative…
What I fight against most in some sense, [when talking to the public,] is the kind of message, for example as put out by the film Good Will Hunting, that there is something you're born with and either you have it or you don't. That's really not the experience of mathematicians. We all find it difficult, it's not that…
It’s a common misconception that someone who’s good at math is someone who can compute quickly and accurately. But mathematics is a broad discipline, and there are many ways to be smart in math. Some students are good at seeing relationships among numbers, quantities, or objects. Others may be creative problem…
Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two…
Why do some children find Math hard to learn? I suspect that this is often caused by starting with the practice and drill of a bunch of skills called Arithmetic—and instead of promoting inventiveness, we focus on preventing mistakes. I suspect that this negative emphasis leads many children not only to dislike…
On a standard piano keyboard, one octave is divided into 7 whole tones: A, B, C, D, E, F and G. In between these tones are 5 further notes which can be called either sharps or flats: A# (Bb), C# (Db), D# (Eb), F# (Gb), G# (Ab). (whether it's a sharp of a flat doesn't really matter, the note has the same frequency…
For some reason that no one really understands, there is a psychological effect upon human listeners in regards to the musical scale. The tonic pitch, or tonal center is not only the mathematical center of the scale, but is the psychological center as well. Human perception of the tonic pitch in relation to the other…
Our earth has orbital motion, revolving once around the sun in about 365 days. Suppose that this orbital motion suddenly stopped completely, but everything else remained the same. How long would it take for the earth to plunge along a straight line into the sun? [...] Kepler's law applies to planetary orbits, whether…
Children learn very early (often as young as 2 years old) to recite the number-word list in order (Fuson, 1988). But at the beginning, the words are merely placeholders—children recite the list without knowing what the individual number words mean. Over time, children fill in the words with meaning, one at a time and…
The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated…
The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 eggs in a carton, 12…
Let’s start by turning back the clock. It is India in the fifth century BCE, the age of the historical Buddha, and a rather peculiar principle of reasoning appears to be in general use. This principle is called the catuskoti, meaning ‘four corners’. It insists that there are four possibilities regarding any statement…
The game is called who’s the best at flipping coins. It’s pretty simple. You flip a bunch of coins and whoever gets the most heads wins. To make this a little more interesting, though, not everybody has the same number of coins. Some people—Team Small—have only ten coins, while the members of Team Big have a hundred…
“Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out—although it might seem that way from what you’ve been taught in courses called mathematics. Those integrals are to mathematics as weight training and calisthenics are to soccer. If you want to play…
Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is…
Mathematics is one of humanity’s great achievements. By enhancing the capabilities of the human mind, mathematics has facilitated the development of science, technology, engineering, business, and government. Mathematics is also an intellectual achievement of great sophistication and beauty that epitomizes the power…