Points and lines, and the relationships between them, are essential ingredients of so many problems in, for example, calculus. In particular, obtaining the equation of the perpendicular bisector of a line segment, dropping a perpendicular from a point to a given line, and calculating the distance from a point to a line are three tasks treated in elementary analytic geometry that recur in the applications....

I spend much of my time traveling for business. These trips often last a week, and we try to visit as many potential customers as possible, and in the most efficient order. This involves matching our hosts' calendars with our own, booking the most cost effective travel options, and coping with last-minute cancellations and changes. It isn’t easy!

This has become so much easier with the advent of shareable calendars and mapping services, like Google Maps. ...

A long while ago, I wrote a couple posts (part1 and part2) about mining data from the US SSA website. I subsequently adapted the code from those blog posts into a visual application with sliders and interactive plots. If you have played with the new ?MapleCloud functionality in Maple 14, you may have seen it posted already.

Back in July of 2005, one of the early Tips & Techniques articles (since updated) in the Maple Reporter was a comparison of two different approaches to fitting a circle to 3D data points. The impetus for the comparison was Carl Cowen's article on the subject. His approach was algebraic - he used the singular value decomposition to obtain a basis for the...

My wife will testify that I am horrible when it comes to keeping things organized and tidy. My colleagues who have seen my office can attest to this as well. My usual defence is that a messy environment is an indication of how busy you are (consequently how productive you are) and basic creativity. But every once in a while, usually when I hit a mental block, I launch into clean up mode to do something completely different hoping that when I’m done, my mental block will be gone. I just went through one of these moments. This time, my cleansing took me to the bottom of one of my office desk drawers to a pile of photos that I had stashed in there ten years ago. Glancing through these, four immediately jumped out and helped me flash back to some key moments in my life. Yes, my 15 minute sabbatical digging through my desk was one of the most productive quarter hours I’ve had in a long time. Here, then, are these four photos that respectively offer a compelling reason to reflect a bit on the past ...

In 1988, Keith Geddes and others involved with the Maple project at the University of Waterloo published a Maple Calculus Workbook of interesting calculus problems and their solutions in Maple. Over the years, I've paged through this book, extracting some of its more unique problems. Recently, I extracted the following problem from this book, and added it to my Clickable Calculus collection, which I use for workshops and web-based presentations.

Three recent articles in the Tips & Techniques series addressed the question of stepwise solutions in Maple. Just what is it that Maple provides by way of stepwise solutions for standard calculations in the mathematical curricula? There are commands, assistants, tutors, and task templates that provide stepwise calculations in precalculus, calculus, linear algebra, and vector calculus. In addition, since Maple can implement nearly any mathematical operation, any stepwise calculation can be reproduced in Maple by assembling the appropriate intermediate steps, just as they would be assembled when working with pencil and paper.

I have to thank my friend John Wass, an editor from Scientific Computing magazine who began a recent article with the clear warning “Attention Engineers! The developers at Maplesoft rarely sit still for very long.” This was a comment on the thrilling speed that enhancements are flowing from the MapleSim pipeline. Although his quote refers to a MapleSim 3 article he wrote, I chuckled as the sentiment still rings true as my colleagues and I catch our breaths after the recent release of MapleSim 4. Yes, the engineering community has definitely taken notice that MapleSim, in such a short amount of time, is already making a big difference in the way we do and think about modeling.

Our solar system was created in three hours… well, at least that was how long it took for me to create a model of it in MapleSim. This process started out as an inquiry from a MapleSim user asking if MapleSim can be used to model planetary motions, through the use of Newton’s law of gravity. I view this kind of inquiry as both a challenge (any time someone asks “can MapleSim do such and such” it is an automatic invitation for us Applications Engineers to try it out J ), and an opportunity to learn new things.

While I am somewhat fascinated by astronomy (who isn’t dazzled by all of those pretty photos of various celestial bodies in the universe?!), I have never developed a keen interest in it. That can be partially attributed to the fact that I grew up in a city that never sleeps, which means serious light pollution (I didn’t realize how beautiful the night sky was and how bright the stars can be until my teenage years on a family camping trip… but that’s another story). The aspect of astronomy that I understand tells me that the law of gravity applies, to a certain extent, and that the magnitude of the numeric values that we are dealing with (for planetary motion simulation) is astronomical! So for me, these are the two key issues that will need to be addressed when creating a MapleSim model.

Sometimes the obvious escapes me, and it’s only due to some chance observation that I realize the same fundamental principles are everywhere.

A short time ago, I created a simple hydraulic network in MapleSim, and after experimenting with some of the parameters, found it gave the same behaviour as an electric circuit I’d modeled earlier.

Some calculus texts compute volumes of solids by the method of "slices" before they discuss the methods of disks and shells. On the other hand, there are texts that start with disks and shells, then throw in a few examples of slices. In any event, these calculations are supposed to be illustrations of how definite integration is an additive process. Unfortunately, students often get lost in the details of the individual examples, and fail to see that all these calculations are just demonstrations that definite integration is a process of addition.

Do an internet search on "Challenger Puzzle" and you will find descriptions and solvers for a puzzle that involves sums of integers from one to nine. Indeed, on a 4 × 4 grid where sixteen integers would fit, four are given, along with the row, column, and diagonal sums of the numbers not shown. The object of the puzzle is to discover the missing twelve numbers.

Unlike Sudoku, the digits can repeat. And unlike Sudoku, the puzzle can have multiple solutions. In fact, "There may be more than one solution" is explicitly stated below the directions, copyrighted by King Features Syndicate, Inc., that appear in my local newspaper, the Waterloo Region Record.

After years of dreaming, planning, scheming, and hoping, my family, as a single entity, finally made it to Asia for a holiday. In our region, school children typically enjoy a mid March “Break”. This usually means families packing up their minivans and driving to Florida or other warm places to help them forget the bleakness of the Canadian winter. This year, however, the spring winds took my family to Asia – Japan and Korea to be specific. I was born in Korea but moved to Canada in 1971 when I was 7 years old. And those of you who have glanced at my past posts know that I’ve been a frequent business visitor to Japan many times over the years. But a family trip to these dynamic places is a completely different experience. There is something remarkable about the discovery experience you get as a pure tourist where issues of punctuality and protocol disappear and you’re left with the experience in its most raw and engaging forms.

Recently, I received an email from a physics instructor asking for help in building a tool that would display the solution of the initial value problem

with the four parameters under the control of sliders. (Of course, we recognize that this equation governs the damped, driven linear oscillator, and that the request to endow its solution with sliders is in service of visualization of the change in the nature of the solution as the parameters vary.)

A few days ago I asked my wife what she thought was the most important invention of the last 100 years. Without pause, she responded “the credit card!”

I suppose that “important” is relative, but my answer is the transistor. As Wikipedia puts it, “The transistor is the fundamental building block of modern electronic devices, and its presence is ubiquitous in modern electronic systems.” Semiconductors are vital to everyday life because they have radically reduced the size, cost and power consumption of all modern electronics.

Life wouldn’t be the same without transistors (or without credit cards, admittedly). Your laptop would weigh hundreds of pounds and be a “mainframe” computer without transistors. Your television would rely on tubes, and you couldn’t mount it on the wall – it would weigh 100 pounds or so without transistors. No mobile phones, either – your telephone would have a rotary dial, and the handset would be connected with a wire. Telephone directories would still be printed books weighing 5 pounds or so.

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