Jonathan Thomson's web journal

How Big is Lily Pad Lake? November 4, 2012

Filed under: Uncategorized — jethomson @ 8:53 pm

Here’s a common brain teaser:

“In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?”

 

Many people answer a bit too quickly and say 28 days. However, the correct answer is 47 days assuming the doubling on the 48th day doesn’t overshoot the area of the lake. On the 47th day the lily pads cover half of the lake and on the 48th day they double covering the entire lake. But what I’m really interested in is how big is Lily Pad Lake?

 

Let’s denote the area of lily pad Lake by A.

 

Then the area covered by the lily pads on the 48th day is A. Therefore the formula for determining the area covered by the lily pads on day n is:

 

On the 48th day Alily is equal to A, and on the 0th day Alily = A/(2^48). The problem doesn’t state how many lily pads are present on the 0th day, but to minimize the size of Lily Pad Lake I’ll assume just one lily pad is present. Thus on the 0th day Alily is equal to the area of 1 lily pad. Assuming the area covered by one lily pad is 5 square feet, then:

 

That’s 1.4 quadrillion square feet or 50,482,628 square miles or 130,749,410 square kilometers. For comparison purposes the Pacific Ocean is 155,557,000 square kilometers and the next biggest ocean is the Atlantic at 76,762,000 square kilometers. So perhaps a better name for Lily Pad Lake would be Lily Pad Ocean, which would have to be a freshwater ocean since lily pads don’t live in salt water.

 

 

Notes
Typical [lily pad] plant size 5-10′ square

The Pacific Ocean is 155,557,000 sq km

 

Greek Letters Used in Mathematics, Science, and Engineering November 18, 2010

Filed under: Uncategorized — jethomson @ 1:25 am

A couple of years back I put a good bit of work into the Wikipedia article Greek letters used in mathematics, science, and engineering. It discusses the Greek letters’ pronunciation, typography, and the concepts they are used to represent. I wish I had a resource like this in engineering school because I would sometimes forget what a letter was called and often wonder if I was using the prefered letter for a variable or parameter in my equations. Here’s another link to A Sky and Telescope How To with an English audio pronunciation guide of the Greek letters.

 

Enable Octave to Read 16 bit Images August 22, 2010

Filed under: Uncategorized — jethomson @ 4:05 am

This how to is a set of instructions for rebuilding libgraphicsmagick so it can process 16 bit images and rebuilding octave so it can take advantage of the new graphicsmagick libraries. This document assumes you’ve already installed octave using a package manager so that all of it’d dependencies have been resolved. Read over the entire how to before executing it. I do _not_ recommend you copy and paste it as a shell script and run it. Pay attention to each step and examine each command before hitting enter; I may have made a few typos.

su -c "apt-get install build-essential fakeroot"
su -c "apt-get build-dep libgraphicsmagick++3"

mkdir -p ~/src_tmp/{gm,oct}/src_pkgs
cd ~/src_tmp/gm/src_pkgs
apt-get source libgraphicsmagick++3
mv ~/src_tmp/gm/src_pkgs/graphicsmagick-1.3.12 ~/src_tmp/gm
cd ~/src_tmp/gm

#copy the following text into a file named rules.patch and save in ~/src_tmp/gm
--- graphicsmagick-1.3.12/debian/rules  2010-08-22 00:36:45.000000000 +0000
+++ debian/rules        2010-08-22 00:42:03.000000000 +0000
@@ -64,6 +64,7 @@
 
        CFLAGS="$(CFLAGS)" CXXFLAGS="$(CFLAGS)" LDFLAGS="$(LDFLAGS)" \
            ./configure $(gm_confflags) \
+               --with-quantum-depth=16 \
                --enable-shared \
                --enable-static \
                --enable-libtool-verbose \
#end copy
patch -p0 < rules.patch
cd ~/src_tmp/gm/graphicsmagick-1.3.12
debuild -i -us -uc -b
cd ~/src_tmp/gm

# install packages that resulted from debuild: 
# libgraphicsmagick++3 and libgraphicsmagick3 are required to run the octave binary
su -c "dpkg --install libgraphicsmagick++3_1.3.12-1_i386.deb libgraphicsmagick3_1.3.12-1_i386.deb"

# libgraphicsmagick++1-dev and libgraphicsmagick1-dev are needed to build octave from source
su -c "dpkg --install libgraphicsmagick++1-dev_1.3.12-1_i386.deb libgraphicsmagick1-dev_1.3.12-1_i386.deb"

# now start rebuilding octave from source
cd ~/src_tmp/oct/src_pkgs
apt-get source octave3.2
mv ~/src_tmp/oct/src_pkgs/octave3.2-3.2.4 ~/src_tmp/oct
cd ~/src_tmp/oct/octave3.2-3.2.4
debuild -i -us -uc -b
cd ~/src_tmp/oct
# install packages that resulted from debuild: octave3.2 and octave3.2-common
su -c "dpkg --install octave3.2_3.2.4-6_i386.deb octave3.2-common_3.2.4-6_all.deb"\
 

Handheld VDG on Instructables March 2, 2010

Filed under: Uncategorized — jethomson @ 11:17 am

I just posted an instructable on how to make a handheld Van de Graaff generator similar to the Fun Fly Stick. Follow this link to instructables’ site or download the pdf to read all about it.

Here’s a short video of a light bulb taped to the collector of the VDG. When a spark is drawn through the bulb the argon inside turns into a violet-blue plasma.