Single digit numbers start at zero and end in nine. We are using only TEN single digits. After nine, we have 'one' ten and no more ones— To do a number trick to guess someone's age, start by asking them to use a calculator to multiply the first number of their age by 5. Then, have them add 3 before doubling the answer.
Next, they should add the second number of their age. In particular, if we take any circle, then is the ratio of circumference to diameter. Imagine the surprise, then, in the midth century, when Leibniz discovered the following extraordinary connection between and the odd numbers :.
While it is possible to prove this result, beyond all doubt, using the methods of calculus, I have yet to meet anyone who can explain this connection between circles and the odd numbers in truly simple terms. The ellipse, for instance, is a curve that was well known to Greek mathematicians, and it can be constructed by pulling a loop of string round two fixed points.
These points, H and I, are called focal points. At first sight, perhaps, this is "just" geometry. Yet, some 1, years after the ellipse's first appearance in this way, the German astronomer Kepler discovered that the planets move around the Sun in elliptical orbits, and - as if that were not coincidence enough - the Sun is always at one of the focal points! And explaining this elliptical planetary motion in terms of a gravitational force on each planet towards the Sun was eventually to be the cornerstone of Newton's most famous work, the Principia.
Yet I suppose the greatest mathematical surprise I've ever had came one rainy November afternoon in , when I found myself proving a strange new theorem. I was trying to give a new twist to an old problem in dynamics, first studied by Daniel Bernoulli in He had considered a hanging chain of several linked pendulums, all suspended from one another, and discovered various different modes of oscillation.
My theorem showed how it is possible to take all these linked pendulums, turn them upside-down, so that they are all precariously balanced on top of one another, and then stabilise them in that position by vibrating the pivot up and down. The upshot of the theorem which appears on the blackboard in the Steve Bell cartoon at the beginning of this article is that the "trick" can always be done if the pivot is vibrated up and down by a small enough amount and at a high enough frequency.
Computer simulations suggested that the upside-down state could in fact be very stable indeed, and this was borne out when a colleague of mine, Tom Mullin, confirmed the theorem experimentally. The photograph below shows an upside-down 50 cm triple pendulum, with the pivot vibrating through 2cm or so at about 40 cycles per second, and the chain of pendulums is seen wobbling back towards the upward vertical after a fairly severe initial disturbance. As soon as we started calling this gravity-defying experiment "Not Quite the Indian Rope Trick" we found that newspapers, radio and TV all began getting interested, and Tom and I have had a great deal of fun with this topic over the years.
My scientific papers on the subject have even been acquired by the archives of the Magic Circle in London, which would surely have astonished a certain year old boy in The papers are kept, I understand, in a box file called Sundry Ephemera. In the end, though, it is not all that important whether mathematics might or might not explain a particular magic trick. What matters, surely, is the extent to which surprising results like this may help persuade the wider public that mathematics, at its best, has a certain magic of its own.
This is a shortened version of an article that appeared in the European Mathematical Society Newsletter, Issue 49, David Acheson's latest book " and All That" Oxford University Press is an original attempt at bringing some of the ideas and pleasures of mathematics to a wide public, and is a Plus favourite.
Your can read our review in issue 23 of Plus , and further details may be found at David Acheson's homepage. Recently, David Acheson gave a lecture in Cambridge on the topics covered in this article, and more.
The lecture was filmed by Science Media Network, and is available to watch online. I think you thought - was ! Difference between 8 and 4 in column 1 and 3, difference between 7 and 7 is zero in the middle I bet that's what you did She also has a great about about to blow the qubic theory.
A Japanese mathematician? Fukimara or similar described the numbers that reappear if their digits are summed, that number reversed and those added. Many know 91 is 3 cubed plus 4 cubed; it is also 6 cubed plus -5 cubed.
Just did this with my 11 year old boy. When he calculated the answer I asked him to take his book, turn to page and find line 9.
In this post, we are going to learn math trick which we will call magic , a trick I learned at BasicMathematics. Before we discuss why the math trick works, let us observe what happened when we subtracted the digits of the numbers in step 3. Take note of these observations because they are the keys to the proof why the math trick works. The condition states the digits of the number chosen in Step 1 is decreasing.
Now, it follows that when digits of the number is reversed, the ones digit of the subtrahend is larger than the ones digit of the minuend. When a 3-digit number is reversed, the tens digit of the original number and the number with reversed digits are always the same. The tens digit of is 8 and the tens digit of is 8. In the subtraction, we have borrowed 1 from 8 when we subtracted the ones digit, so the tens digit of the subtrahend is greater than that of the minuend.
In fact, this is always the case Why?
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