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Then the watch face is split equally into three parts.īruted it out in VBA and found the very closest times at which the three segments are closest to 1/3 of the face:Ĭonsider the clock face divided into 12*3600 units. It doesn't matter which is which, but rank the angles of the dials. We can find out the angle of each clock dial. Let's also assume that all numbers are modulo 360. Let's assume the noon direction is angle 0, with positive angles in the clockwise direction.
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None of those times equally divide the clock face. There is no perfect integral or congruence given the ratio with the 3 hands of a clock to form an equal 3 part division. However, the second hand must also be at 12 at those times. The hour hand at 4 and 8 would have the minute hand pointing at 12. Until next time, enjoy whatever you learn.ħ Comments on “IntMath Newsletter: Piano trig applet, continued fractions”Īn equal 3 part division for the hands of the clock would be 120 degrees (360/3). One of the secrets of life is that all that is really worth the doing is what we do for others. How about for any other cases (like close to 01:45:30, or 02:50:35)? Is it true? Can you prove your conclusion for the clock at any time? When the second hand reaches somewhere close to 20 seconds past the minute, the clock face will be divided into 3 equal parts. True or false? Consider a clock at 11:40 AM. Apart from being a well-known author, Carroll (real name Charles Lutwidge Dodgson) was a mathematician, logician, Anglican deacon, and photographer. The walking problem was based on one by Lewis Carroll, author of Alice in Wonderland, and Through the Looking Glass. The puzzle in the last IntMath Newsletter asked how far a person walked given some (seemingly) insufficient conditions.Ĭorrect answers with explanation were provided by Chris, Thomas and Nash. In this short TED-Ed video we get some good pointers on what one million really looks like. It's not surprising as most of us don't use them every day, but as we do hear about them constantly on the news, it's important to get a good conception of them.
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Math movie: How to visualize one part per millionĪ lot of people struggle with very large (or very small numbers). New 3-D structure shows optimal way to divide spaceĤ. Researchers in 2016 discovered a new 3D structure that divides space into 24 regions, and have shown that it is the best solution yet to a modified version of a geometrical space-partitioning problem that has challenged researchers for more than a century. Some Belgian mathematicians had some breakthroughs on this issue last year. How can space be partitioned into 3D structures of equal volume in a way that minimizes the total surface area of each structure? Lord Kelvin (the temperature guy) asked in 1887: Mathematicians have studied space filling for some years, especially since They need to display their wares attractively, safely and in a space-efficient way. It contains many worked examples and several online calculators and it's by Richard Knott, Surrey University:įruit shop owners know a thing or two about space filling. This extensive resource covers continued fractions. We stop at that last line because there is a remainder of 0, and we conclude the GCD is 3.Ĭontinued fractions are a special form of fraction and can be used when finding GCDs, as well as in many other applications like finding square roots and solving quadratic equations. For example, the GCD of 93 and 42 would be found as follows: You may recall the Euclidean Algorithm for finding the greatest common divisior of 2 numbers. Here's some background on what's going on:įrequency of notes on a piano - interactive learning object 2. Frequencies of notes on a piano - interactive learning objectĮxplore piano note frequencies in this new interactive learning object, combining trig graphs and exponential growth.įrequency of notes on a piano - interactive learning object New applet: Piano note frequencies interactiveĦ.