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Today's quote is from the cat in The Cat in the Hat by Dr. Seuss.
"... 'I will show you
another game that I know!'
and then he ran out.
and, then, as fast as a fox,
the Cat in the Hat
came back in with a box.
A big red wood box.
It was shut with a hook.
'Now look at this trick,'
said the cat.
'Take a look!'
Then he got up on top
With a tip of his hat.
'I call this game FUN-IN-A-BOX,'
said the cat.
'In this box are two things
I will show to you now.
You will like these two things,'
Said the cat with a bow.
'I will pick up the hook.
You will see something new.
Two things. and I call them
Thing One and Thing Two.
These Things will not bite you.
They want to have fun.'
Then, out of the box
came Thing Two and Thing One!' ..."
I teach the idea of conjugates quite often in my classes. Conjugates are two arithmetic expressions that involve two values. As an example, let's suppose I use the two values, 9 and 5. Conjugates using these two values would be: 9 + 5 and 9 - 5. Conjugates are simply two expressions that are formed by adding and subtracting the values in the same order. Conjugates can be generalized to a + b and a - b whose product becomes a^2 - b^2 which math geeks refer to as the difference between squares. A few examples of conjugates that are utilized in mathematics are: confidence intervals (statistics), complex solutions (analytical algebra), and rational expressions containing square roots (limits/calculus).
Today has always been a special day for me. As a child, this day signified the beginning of the holiday season. I marked these dates on my calendar: October 23, October 31, November 22-28, December 25, and January 1. I am sure that four of the five dates listed are obvious to the reader and many may presume that with a mathematics background that I am championing today's date as Mole Day, but the reality is today is my brothers' birthday. I have brothers that are identical twins.
In fact, my brothers are mirror twins. Bruce is right-handed and Bill is left-handed. When I study their facial features, Bruce resembles my mother's side of the family and Bill, of course, my father's. On their birthday, my mother would make a white angel food cake for one and a chocolate devils cake for the other. I was in culinary heaven, two slices in one day! The holiday season had begun!
I have always felt their relationship is one of the strongest I have every encountered. My sons have often mentioned that when Bruce and Bill are together, the sum is much greater than the parts. In my classes, I use stories of my family to form connections to mathematics. I refer to Bruce and Bill as the conjugate twins.
In my blog, The Fabulous Five, I noted that the interactions we have with our siblings shape our personalities. My grandmother would describe to me the befuddlement that overcame me as a toddler when my mother came home with twin babies. I don't really know how much I understood of the complexity that just entered my life as a 18-month-old child, but I would agree their births changed my life significantly from that moment. I was transformed in a short period of time from the baby of the family to something different, not necessarily the middle child but not exactly the oldest either. Like Thing One and Thing Two, two creatures had entered my domain that would bring a new thrilling energy that was a mixture of frustration, fear, and sheer enjoyment.
My brothers became my playmates and my rivals. In the next 16 years, I learned to be competitive, cooperative, assertive, compromising, creative, imaginative, empathetic, and manipulative. We were explorers, warriors, athletes, and builders. We crawled through culverts, shot imaginary intruders with sticks and broken baseball bats, and played endless games of baseball and football. Our teams were easily decided--the twins versus me. We adjusted rules so that two-on-one games were possible through a series of arguments and heated discussions. Any disputes evaporated in our nightly dreams and we began each day anticipating a renewed adventure.
Today, I will celebrate the birth of the Conjugate Twins, Bruce and Bill. I will raise a toast in their honor, give them a call, and enter the holiday season thankful for the impact they have had in my life.
Today has always been a special day for me. As a child, this day signified the beginning of the holiday season. I marked these dates on my calendar: October 23, October 31, November 22-28, December 25, and January 1. I am sure that four of the five dates listed are obvious to the reader and many may presume that with a mathematics background that I am championing today's date as Mole Day, but the reality is today is my brothers' birthday. I have brothers that are identical twins.
In fact, my brothers are mirror twins. Bruce is right-handed and Bill is left-handed. When I study their facial features, Bruce resembles my mother's side of the family and Bill, of course, my father's. On their birthday, my mother would make a white angel food cake for one and a chocolate devils cake for the other. I was in culinary heaven, two slices in one day! The holiday season had begun!
I have always felt their relationship is one of the strongest I have every encountered. My sons have often mentioned that when Bruce and Bill are together, the sum is much greater than the parts. In my classes, I use stories of my family to form connections to mathematics. I refer to Bruce and Bill as the conjugate twins.
In my blog, The Fabulous Five, I noted that the interactions we have with our siblings shape our personalities. My grandmother would describe to me the befuddlement that overcame me as a toddler when my mother came home with twin babies. I don't really know how much I understood of the complexity that just entered my life as a 18-month-old child, but I would agree their births changed my life significantly from that moment. I was transformed in a short period of time from the baby of the family to something different, not necessarily the middle child but not exactly the oldest either. Like Thing One and Thing Two, two creatures had entered my domain that would bring a new thrilling energy that was a mixture of frustration, fear, and sheer enjoyment.
My brothers became my playmates and my rivals. In the next 16 years, I learned to be competitive, cooperative, assertive, compromising, creative, imaginative, empathetic, and manipulative. We were explorers, warriors, athletes, and builders. We crawled through culverts, shot imaginary intruders with sticks and broken baseball bats, and played endless games of baseball and football. Our teams were easily decided--the twins versus me. We adjusted rules so that two-on-one games were possible through a series of arguments and heated discussions. Any disputes evaporated in our nightly dreams and we began each day anticipating a renewed adventure.
Today, I will celebrate the birth of the Conjugate Twins, Bruce and Bill. I will raise a toast in their honor, give them a call, and enter the holiday season thankful for the impact they have had in my life.
