Today is Mardi Gras. For several years I eagerly anticipated all
the parades and parties. This year I only attended three of the dozen
or so evenings of parades – and ended up leaving two of them early.
The desire to grovel for beads just wasn’t there this time. The
last two Mardi Gras were a blast, and after a rude introduction to New
Orleans they helped me start developing a sincere affection for this city.
Along with a collection of wonderful experiences during my almost4 years
here though, the baggage is also accumulating. I believe I’m just
one more bad memory away from looking for somewhere else to live.
In the same way I encourage my older students to leave the state for
college and experience life outside of Louisiana, I still don’t
feel like I’ve seen very much of this country or the world myself.
In my relationship with NOLA, sitting out most of this Mardi Gras is my
version of not calling back after a date. When I do decide to end it,
I hope the “relationship” will just dissolve with no hard
feelings.
(Really NOLA, you’re a very nice city and you deserve
the best… It’s not you, it’s me… We can still
be friends… Just gimme back my stuff…)
Ironically, I’ve poured countless hours into my job this year
trying to develop and refine my Algebra 2 and Calculus lessons to a point
where I can just “pull them off the shelf” next year with
minimal prep time required. By the end of last school year I felt like
I was just beginning to really learn how to effectively utilize the electronic
whiteboard, document projector, and other technological resources I’ve
been provided. As a result this year I’ve completely revamped many
of last year’s earlier lessons, which has taken quite a bit of time.
Pretty soon the school will ask the faculty to sign letters of intent
to return for next year. I’ll most likely sign it, if for no other
reason than to take advantage of all the extra effort I’ve put in
this year. Meanwhile though, the search for “what next” may
pick up momentum.

3.5
years of UNO – shoot, I could’ve Photoshopped this up
in 15 minutes 
In January I picked up my diploma for a M.Ed. in Curriculum and Instruction
from UNO. As much as I wanted to finally relax for a semester with no
nonLusher obligations, I had already agreed to sign on as an adjunct
instructor to teach a Technology in Secondary Mathematics course for the
same Teach Greater New Orleans program through which I earned my certification.
I’ve enjoyed the course so far, and am glad to now be on the “other
side” of the rookie year of public school teaching. Memories of
my first year get aroused when we meet every week, and I’m probably
more sympathetic in determining the workload for these twelve math teachers
than the instructors for the other disciplines. Feedback I’ve received
so far has been very positive, although there’s much more that I’d
like to share with them. However I know firsthand that there’s
only so much knowledge that can be crammed into an emotionally spent human
brain, so my simple goal is for them to finish the class saying, “That
was useful, and the workload did not utterly crush my desire to teach.”
Below are some of the ways in which I’ve tried to spark interest
in my classes. Sometimes the content is an intriguing extension of something
we’re studying, or in some cases it’s hardly related at all.
As long as there’s some connection to what makes math fun for me,
I justify spending the class time.
Conic study






The
premise of this study is simple. Lines are drawn on the axes of
a grid such that as the xvalue of one point gets bigger, the
yvalue of the other point gets smaller by the same amount. I
was surprised to see that drawing all the lines under this condition
resulted in the shape of a parabola. Even when one of the axes
is skewed such that they are no longer perpendicular to each other,
the resulting construction still bounds a parabola.
I
would guess that one of my students from last year may have had
this demonstration in mind when she made the project photographed
above for an art class.
A
paper proof (for the case of perpendicular axes) is included above,
although for some reason students weren't interested in studying
it.
To
recreate this geometry in a browser window, click an a link below.
The files were created with free Geogebra software, although no
software installation is necessary to view them (except possibly
installing/upgrading Java in your web browser). If you see a popup
message, go ahead and "trust" the certificate.

Rational Function study 






I
stumbled across this diversion while covering "Limits at
Infinity (of rational functions)" in my Calculus class.
By tweaking just one of the parameters of a function, some really
cool images appeared.
To
recreate this geometry in a browser window, click an a link
below. The files were created with free Geogebra software,
although no software installation is necessary to view them
(except possibly installing/upgrading Java in your web browser).
If you see a popup message, go ahead and "trust"
the certificate.

Cycloid/Trochoid study 









After
class recently an inquisitive student started to ask me, out
of the blue, what would happen if he rolled his ring around
the outer edge of my bicycle tire. I assumed he wanted to know
about the path traced by a given point on his ring and I excitedly
proceeded to tell him about cycloids and such. It turned out
that this was not his original question, but it was too late
– I was on a roll!
To
recreate this geometry in a browser window, click an a link
below. The files were created with free Geogebra software, although
no software installation is necessary to view them (except possibly
installing/upgrading Java in your web browser). If you see a
popup message, go ahead and "trust" the certificate.
Wikipedia
also has some great info on trochoids,
hypotrochoids,
and epitrochoids.

Buffon's Needle 

In
Calculus recently we came across an exercise in the book concerning
the mathematics behind Buffon's Needle experiment. In this experiment,
a needle is dropped randomly on a planar surface containing parallel
lines. The distance between adjacent parallel lines is equal to
the length of the needle. The question is, what is the probability
that the dropped needle will touch a line? Interesingly, with
enough trials, the probability should approach 2/pi, or about
63.66%.
Click
on the above image to try out my Flash simulation of this experiment.
Wikipedia
has extensive background on Buffon's
Needle.
Even
if unfamiliar with programming, I'd encourage any math student
to check out the complete
code used to make this animation work and attempt to decipher
the math used within it.

Ambigrams 






Mom
recently sent me some books on optical illusions and related topics,
remembering how much they intrigued me as a kid. In one of the
books I saw the work of an ambigram artist, Scott
Kim. It reminded me of the artwork I saw in the book Angels
and Demons, which I then discovered was created by ambigram artist
John
Langdon.
Amgibrams
read either exactly the same when read upside down, or they read
another word or phrase. Given that the movie adaptation of Angels
and Demons is coming out in a few months, I figured this would
be a perfect time to share this art form with my students.
I
tried my hand at making my own ambigrams. Click on any image above
to open in a new window and click on it to animate, except the
clock face (which is linked to a larger version of the still image).

New Lusher Discipline policy 

At
Lusher some dispaly cases have appeared in the hallways recently.
Most students assume that they are for the purpose of showing off
trophies and/or artwork. I'm trying to convince students that this
is all part of a new nononsense discipline policy. 
Mathemagician 

I've
shown this video for the last two years in my class. This "mathemagician"
is incredible, and even mathhaters seem to marvel at his feats.
Yes, I have a new hero. 
Pi songs 

A
few weeks ago one of our history teachers shared with me the song
"Pi," by Kate Bush. I was immediately hooked. I've since
found several other songs about pi, but this is my favorite.
The
song may be heard on youtube.

