Dr. Jason Schattman: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=546
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 28 Nov 2014 17:00:53 GMTFri, 28 Nov 2014 17:00:53 GMTNew applications published by Dr. Jason Schattmanhttp://www.mapleprimes.com/images/mapleapps.gifDr. Jason Schattman: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=546
How Fast Does An Advent Candle Burn?
http://www.maplesoft.com/applications/view.aspx?SID=100332&ref=Feed
<p>Any kid who's ever been entranced by an advent wreath knows that a tapered advent candle shrinks faster on Sunday night when it's new and slender than on Saturday night when it's old, stubby and caked with melted wax. How much faster? As an apropos application of math during this Christmas season, <strong>we derive a formula for the height of a burning tapered candle as a function of time</strong>. Assuming the candle has the shape of a cone when it is new and that it loses volume at a constant rate as it burns, we show that the height of the candle shrinks roughly in proportion to the cube root of time.</p><img src="/view.aspx?si=100332/thumb.jpg" alt="How Fast Does An Advent Candle Burn?" align="left"/><p>Any kid who's ever been entranced by an advent wreath knows that a tapered advent candle shrinks faster on Sunday night when it's new and slender than on Saturday night when it's old, stubby and caked with melted wax. How much faster? As an apropos application of math during this Christmas season, <strong>we derive a formula for the height of a burning tapered candle as a function of time</strong>. Assuming the candle has the shape of a cone when it is new and that it loses volume at a constant rate as it burns, we show that the height of the candle shrinks roughly in proportion to the cube root of time.</p>100332Mon, 20 Dec 2010 05:00:00 ZDr. Jason SchattmanDr. Jason SchattmanParabolic Reflectors and the Ideal Flashlight
http://www.maplesoft.com/applications/view.aspx?SID=5523&ref=Feed
A flashlight projects light in one general direction because of the reflecting surface behind the lightbulb. This redirection of light is called collimation, a fine SAT word if I've ever heard one. A good flashlight collimates more of the bulb's light than a poor one. How well a flashlight collimates depends on the shape of the reflecting surface and on the distance of the bulb from the surface.
Which shape is the collimation champion? This application compares the light-reflecting properties of four different surfaces:
Parabolic
Spherical
Quartic
Conical<img src="/view.aspx?si=5523/thumb.gif" alt="Parabolic Reflectors and the Ideal Flashlight" align="left"/>A flashlight projects light in one general direction because of the reflecting surface behind the lightbulb. This redirection of light is called collimation, a fine SAT word if I've ever heard one. A good flashlight collimates more of the bulb's light than a poor one. How well a flashlight collimates depends on the shape of the reflecting surface and on the distance of the bulb from the surface.
Which shape is the collimation champion? This application compares the light-reflecting properties of four different surfaces:
Parabolic
Spherical
Quartic
Conical5523Thu, 29 Nov 2007 00:00:00 ZDr. Jason SchattmanDr. Jason Schattman"Just Move It Over There, Dear!"
http://www.maplesoft.com/applications/view.aspx?SID=5158&ref=Feed
My mother once asked me if I could please move her living room sofa into the guest bedroom down the hall and around the corner. Before I broke my back dragging this battleship down the hallway only to discover that it wouldn't make the turn, I decided to take some measurements and work out the math first.<img src="/view.aspx?si=5158/thumb.jpg" alt=""Just Move It Over There, Dear!"" align="left"/>My mother once asked me if I could please move her living room sofa into the guest bedroom down the hall and around the corner. Before I broke my back dragging this battleship down the hallway only to discover that it wouldn't make the turn, I decided to take some measurements and work out the math first.5158Wed, 29 Aug 2007 00:00:00 ZDr. Jason SchattmanDr. Jason Schattman