A Walk on a Snowy Day

The deer waited for me to take off my mittens, get my camera out of its bag, adjust the settings and focus. I really needed a different lens for this shot. The falling snow adds a little blur. Here are the Loch Ness Deer.

One of my students has a test next week on transforming functions. Here's a reflection across the x-axis.

The vine is almost a parabola.

Asymptote Anecdote

During a discussion of science jokes with a group of friends, I mentioned that the asymptote is the mathematical model for my writing career. It’s a joke many people don’t get. 

Merriam Webster’s definition of asymptote is "a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line," 

In other words, the curve approaches the line, gets infinitely close to it, yet never crosses it.  

One person asked about the origin of the word. Asymptote likely comes from Greek asymptōtos not meeting, from a- + sympiptein to meet.” (also Merriam Webster) 

To my surprise, I discovered Merriam Webster lists rhyming words. I don’t write in rhyme, but consider the possibilities of billy goat, sticky note, or even quarter note. Here’s Merriam Webster’s list: 

anecdote, antidote, assault boat, billy goat, Capriote, cashmere goat, casting vote, Corfiote, creosote, dead man's float, entrecôte, ferryboat, flying boat, get one's goat, Huhehot, locomote, matelote, miss the boat, morning coat, motorboat, mountain goat, nanny goat, overcoat, paddleboat, papillote, passing note, pedal-note, petticoat, picketboat, polo coat, powerboat, quarter note, redingote, riverboat, rock the boat, rubythroat, Shabuoth, Sialkot, sixteenth note, sticky note, sugarcoat, symbiote, table d'hôte, undercoat, yellowthroat

Thinking About Graphs

Today is the birthday of Rene Descartes. People usually remember him for saying, "Je pense donc je suis." (I think therefore I am.) For me, his most important accomplishment was identifying the relationship between geometry and algebra, thus laying the foundation for analytical geometry. Cartesian coordinates are named after him, although he did not carry his mathematical research far enough to plot a line.

References:
http://www.notablebiographies.com/De-Du/Descartes-Rene.html http://mathforum.org/cgraph/history/descartes.html
http://www.freeessays.cc/db/30/mdg2.shtml
http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes
http://en.wikipedia.org/wiki/Analytic_geometry

A New Prime Number

Math is in the news today!

A new prime number has been discovered by Odd Magnar Strindmo from Melhus, Norway. It is 13 million digits long, so I won't display it here. It is a Mersenne prime number which means it can be calculated from the equation:

where n is a prime number.

The calculation required a lot of computing power (because the values for n are so large) and was aided by the Great Internet Mersenne Prime Search (GIMPS). People can download software onto their personal computers to help with the calculations.

Overheard #55

"There are infinitely many infinities – even more than you can count with the infinitely many infinities."

Lemon Meringue

As part of our Pi Day celebration, my sons lobbied for a lemon meringue pie. I haven't made one in years, so I forgot how much effort is involved. But here it is.

Sam pointed out that we could also celebrate Approximate Pi Day on July 22 because 22/7 is an approximation for π.

I told him that would be Inverse Pi Day. (Think visually.)

"Not in Europe," he said.

We'll see. Perhaps in July, I'll bake an approximate pie.

Happy Pi Day

Today is π Day - March 14 or 3-14. I will arrange for this post to appear at 1:59 AM to get a few more digits into my celebration.

I found some fun links.

pi day site

one million digits of pi

pi facts

cool graphic of a circle unrolling

pi song

Asymptote

Some days I feel that the asymptote is the mathematical model for my writing career.

What is an asymptote? Googling the word results in many links but few clear definitions. An asymptote is a line that a curve approaches, getting ever nearer, but never crossing, even if you extend the curve to infinity. Now the metaphor is obvious.

A favorite example of an asymptote is y = 1/x because it has both vertical and horizontal asymptotes. As you make x smaller and smaller, y gets larger and larger. But when x becomes zero, y is infinity. You can't plot infinity, so you never intersect the y-axis. The same is true for the x-axis, but this blog post is getting pretty nerdy, so I'll stop here.

What is the solution to an asymptotic career? Change the equation!

Three Happy Discoveries

1. I just learned over at Jacqui's Room that today (03-03-09) is Square Root Day. When Math-Kid-Sam gets home from school, I will certainly greet him with that news.

2. Yesterday we saw a marsh hawk roosting on a dead tree in the back yard. I hope she and her mate will decide to nest here. (I was unable to get a photograph.)

3. Thanks to a heads up from Ruth McNally Barshaw, I found Anastasia Suen's blog, Children's Book Biz News. Wow, what a wealth of information!

On Topic

Writing:
I am pondering a new project, brainstorming scenes, sketching characters and enjoying myself - so far. Yes, I know the main character needs a name.

Reading:
Sam said that while his English class is reading Heart of Darkness, he welcomes homework interruptions of all kinds, even requests to shovel the driveway.

Math:
Sam is taking an Advanced Placement calculus class online. I emailed the distance learning institution several times to request the bill. They responded that it would be sent later. I worried that if we never paid, Sam wouldn't get credit for the course. They finally sent the bill; I paid it. We are no longer stealing a calculus class.

Science:
Jeremy's science book states that ATP (adenosine triphosphate) is the most important biological molecule. My husband wondered why they wanted the kids to memorize that little fact because there are at least 500 molecules required for life. I responded that cyanide poisoning is almost instantaneous, and since it works by inhibiting electron transport and thus the production of ATP, organisms die quickest without ATP. Oxygen deprivation takes longer to snuff out the test subject. Then, my husband reminded me that anaerobic bacteria need no oxygen, but do require ATP. That settles it ATP is the most important biological molecule. We agree that Mg+2* is the most important biological ion.

*Again, Blogger thwarts my desire to use superscripts.

Zero

Zero: The Biography of a Dangerous Idea

by Charles Seife

Penguin Books (2000)

If you've always hated math, this book probably won't change your mind. For people like me, who enjoy numbers, science, questions and history, it is a fascinating read.

Seife describes the roll of zero in mathematical history. Early number systems did not include zero because people did not need zero to count sheep or barter grain. Later, zero was banned for religious reasons because accepting zero, meant acknowledging infinity, and numeric infinity threatened Medieval concepts of God. Seife gently leads the reader through calculus, relativity, quantum mechanics and string theory. He finishes by explaining why the universe will end in ice not fire.

In Vino Veritas

In wine is truth, or at least in wine is calculus.

Johannes Kepler* helped invent calculus while calculating the volume of wine kegs. In 1612, wine came in kegs, not 750 ml bottles, and Kepler was concerned because the method used to estimate the volume of these kegs was inaccurate.

The volume of a cylinder is simply the area of the base times the height. (V = πrrh)** This formula can’t be used to determine the volume of a keg because of the bulgy parts on the sides. Kepler imagined slicing the kegs into infinitely thin sections. He calculated the volumes of the sections and added them up. Not only did he get a pretty good answer, he devised the precursor to taking an integral.

This story and many others about the history of mathematics can be found in Zero: the biography of a dangerous idea by Charles Seife. (Penguin Books, 2000)

*In case you think Kepler was just an old sot, he also figured out that the planets move in elliptical paths.

** I couldn't make the "r squared" notation with a superscript 2 in Blogger.

Since Time Began

I am reading Zero: The Biography of a Dangerous Idea by Charles Seife. I'll review it when I finish, but last night I encountered a factoid that I couldn't wait to share.

Most early number systems were base-5, base-10 or occasionally base-20 because they were handy. The early Babylonians used base-60! That means if a Babylonian wanted to count on his fingers, he needed the help of two friends, and none of them could wear shoes.

I have been wondering for a long time why time is base-60. I remember, as a kid, asking my dad why hours and minutes were divided into 60 not 100 parts. He didn't know. He told me people had tried to institute a time system based on 100, but it didn't catch on. Now I know why there are 60 minutes in an hour. We can blame the Babylonians.

Tangent to the Curve

My husband and I grew up in costal towns in Southern California where picturesque roads wind around the hills above the ocean. When we moved to Michigan, we thought nothing of buying a house located on a curve. We neglected to consider snow and ice.

Even though we live in a quiet subdivision where snowplows seldom venture, people tend to drive too fast, and when they skid, their trajectory intersects with our mailbox. Last Friday, a car skated around the corner, hopped the curb, leaped the sidewalk and landed on our front lawn. Fortunately, our mailbox lived to fight another day.

Lori, here’s a link for tangent.

Mount Everest Math

At the assisted living facility where my mom lives, one of the physical therapists proposed the Mount Everest Challenge. He claimed staff members could climb the equivalent of Mount Everest by taking the stairs a certain number of times.

When I visit my mom, I always climb the stairs to her 5th floor apartment. But somehow the Mount Everest Math seemed wonky to me. Today, I finally got around to redoing the calculations.

Sparing you the details of the math, I climb 33.25 feet to visit my mom. Mount Everest is 29,029 feet above sea level or 873 trips up the stairs. Assuming I visit her every day, it will take me about 2 years and 5 months to reach the top of Mount Everest.

But wait! Most climbers, taking the southeastern ascent, fly into Lukla (9,400 feet) then hike up to Base Camp (17,700 feet). The climb from Base Camp to the summit only requires 340 trips. I’m way past that. I’ll have made the climb from Lukla by next February.

How many people have carried laundry up and down Mount Everest?

Photo from Getty Images

Homework Help

This afternoon my younger son asked me about transitional sentences. I offered what I thought was a cogent explanation. He said, "I thought you were supposed to be good at writing."

Then I looked over his geometry homework. The book explained that mathematicians do not draw using perspective. What? All these years of drawing cones, cubes and prisms and I never realized I wasn't using perspective! Well, my shapes are drawn in perspective, if the vanishing point is infinity.

Conversation snippet:
Me: Don't you think infinity is blue?
Husband: Only during the day.

Hodgepodge

On Reading

Lately, I haven't read a book that swept me away. I don't know if I'm cranky, or if my library-shelf-perusal-time has been rushed. I wanted to find a stellar book to review on Write Brainers. No luck, so far. I'll have to keep searching. (tough job, but somebody has to do it)

Paula Payton introduced me to a cool website for keeping track of books. Goodreads can be used to record and/or review books, or to hold book discussions with a group. I'm part of a book discussion group from SCBWI-MI, although, I'm not sure I'll take time to post additional opinions of our books of the month. The site does keep an orderly list of the books I've read. It also displays cover art which a simple Excel file wouldn't do.

On Writing

I haven't encountered a lightning moment, but I've enjoyed many small flashes of insight. Lightning bugs? I hope, someday, the total lumens will add up to a revised novel.

I'm about to pull up my socks and submit the first two chapters of my work-in-progress for a paid critique at the SCBWI-MI spring conference.

On Arithmetic

Paid critiques at conferences are awarded by lottery. Statistically speaking, the chances of me getting one are small. There are 8 slots for one-on-one critiques, and about 150 people will attend the conference. Here is where the math gets blurry. I don't know how many of the 150 would want a critique, and how many are ineligible because they received a critique at last fall's conference. Still, what do I have to lose?

Skunk Cabbage

Photo by Z.F. Burton

My new revision idea isn't working. The concept looked pretty from a distance, but when I got close, I discovered it stinks. Thus, the skunk cabbage. What I need now is a better idea, a lightning moment, a flash of clarity. My husband says, "Sometimes you have to bang your head on something for a long time before you start to see lights." Bang. Bang. Bang.

On a lighter note, the center of the cabbage depicts a Fibonacci sequence. (Look at the diagrams at the right of the link.)