Thursday, December 23, 2010

Toasting Time is Still not Linear

Well, I've finally completed my toaster experiment.  I went through three loaves of bread and four or five days.  My family is happy to have me back.

First, a bit about the toaster.  The settings run from zero to five on the toaster.  Between each number, the dial is divided into four equal parts.  To get the toaster setting for the data, I took the setting on the dial as a fraction and multiplied by four.  That is why the data runs from 1 to 19.5 in the spreadsheet.  I used 19.5 instead of 20 because the dial wouldn't turn that far.
The International Standard Toaster


I made sure to go through each of the settings on the toaster.  The order was scrambled by a Python program.  I did write down one of the numbers incorrectly, so I did four trials on setting four, and two trials on setting fourteen.

I used a stop watch to time the toaster.  I rounded the toasting time to the nearest second.  After each trial, I let the toaster cool to 27 degrees Celsius.  That is to ensure a consistent starting temperature.

For each trial, I weighed the bread before and after toasting.  This is to measure the percent loss of mass during toasting.  My hypothesis is that most of the mass loss is due to the water in the bread evaporating in the toasting process.

The raw data can be downloaded from Google Docs at this link.  The graphs of the data are below.
Time (sec) vs. Toaster Setting
Percent Decrease in Mass vs. Toaster Setting
Percent Decrease in Mass vs. Time (sec)
I haven't applied any regressions to the data yet.  I am planning on doing so in the next couple of days.  I will let you form your own opinions first.  The only conclusion I will draw at the moment is that the toasting time is not a linear function of the toaster setting.

Tuesday, December 21, 2010

Happy New Year!

I know we're ten days from the ball dropping in Times Square.  Today is the winter solstice in the Northern Hemisphere.  This means that today will have the sun visible for the least number of hours this year.

Since calendars are arbitrary, we might as well declare the winter solstice to be the start of the year.  My Mother's family has be celebrating the winter solstice for a few years.  There are different observances in different cultures.  You can find on list on www.timeanddate.com and another on www.religioustolerance.org.

So, at 6:38 (Eastern Time) countdown to a new year.

Wednesday, December 15, 2010

Video Proof That I'm Not Dead

Yesterday, I finished grading for the semester.  I can now worry about Christmas.

As part of the Title III grant for distance learning, I recorded a short introductory video for my Intermediate Algebra class.  We teach Intermediate Algebra as a hybrid class because it is four credits, which interferes with the scheduling of other classes.  The video is on YouTube, but you can watch it here.  The excellent production was done by Justin Dean.

Thursday, December 9, 2010

Warming up to Python Programming in the Classroom

Last month, I commented on Dan Meyer's blog dy/dan that I wasn't sure about using programming as part of teaching mathematics.  Dan had worked on a project of developing Python programs to be part of the mathematics curriculum.  This was part of a Google project on computational thinking.  I've played around with Python, and I like what I see so far.

I started writing a Python program as part of my toaster data collection.  I wasn't happy with using a die to choose the toaster settings because one setting came up more than the others.  Instead, I wanted to test all of the settings in a random order.

I have programmed enough to be able to implement this program in several different languages.  However, I didn't want to take the time to write it in C or Java.  I started to write a program on my TI-83, but that was too slow.  I remembered that my friend Shawn was working on learning Python, so I thought I would give it a try.  It took me half and hour to download Python, install it, and learn enough to get the result I wanted.  I would like to claim that a short development time was due to my genius.  However, it had to do with the random.shuffle() function which was built into the random module.

Now that I see how fast one can develop a program in Python, I am intrigued by the possibilities.  I am discovering that there are many third-party extensions that could be helpful in the classroom.  I am looking forward to exploring their use over Christmas.

Tuesday, December 7, 2010

Toasting Time is Not Easy

A couple of posts ago, I noted that the data collected by Dan Meyer indicated that a linear model is not the best fit for modeling the time spent toasting vs. the toaster setting.  I've been collecting some data of my own, and it does not look pretty.  The rough data is below.  Remember that the toaster settings were chosen (mostly) randomly.
Raw Toaster Data


From the graph below, it is easy to see there is a lot going on.
The Linear Regression for the Data
The problem with the data is the settings between 2 and 10, which looks linear with a different slope than the settings above 10.

The exponential model is listed below.  It is just a bit more accurate, but not noticeably.
The Exponential Regression for the Data

Finally, for your approval is the cubic regression.
The Cubic Regression for the Data

Well, it's back to the toaster.

Friday, December 3, 2010

Carl Sagan in 1995

I stumbled on this video tonight.  It's an Charlie Rose interview of Carl Sagan.  The thought of life off of Earth has been on my mind for a couple of days since this NASA announcement.  Enjoy.

Wednesday, December 1, 2010

If You Were Wondering About the Density of Diet Mnt Dew

We were reviewing fluid forces in Calculus II today.  I decided to give an example using items from the room.  The first fluid I found was my Diet Mnt Dew (the "Mountain" was replaced by "Mnt" a while ago).  The mass density is 901 kilograms per cubic meter.  The weight density is 8830 Newtons per cubic meter.

One of the students asked if the density would change as the carbonation is released.  Our chemistry professor at the college said that the density would change, but not enough to be noticeable.