Posts tagged ‘ratio’
Russell, Robertson, and Ratios
In the NBA, a tripledouble happens when a player has a doubledigit total in three of the five categories (points, assists, rebounds, steals, and blocks) in a game. Tripledoubles are very rare; on average, one has been recorded only once every 27 games since 2003. So far this season, there have been 111 tripledoubles throughout the entire NBA — and Russell Westbrook has 41 of them.
In 196162, Oscar Robertson set a record that Westbrook is about to break. That year, Robertson recorded 41 tripledoubles in 80 games. Westbrook recorded his 41st tripledouble of the current season in just 78 games. When two fractions have the same numerator, the one with the smaller denominator is larger. Consequently, 41/78 > 41/80, so Westbrook’s accomplishment exceeds Robertson.
But ratios can be used to make the point even more dramatically. In the early 1960’s, pro basketball games were played at a faster pace than they are today. In 1961‑62, the average game featured 126.2 possessions, meaning that Robertson typically had more than 60 tries to grab a rebound, make an assist, or score some points. By comparison, there have been an average of just 96.4 possessions per game during the current NBA season, meaning that Westbrook generally has fewer than 50 attempts per game to improve his stat line. So another ratio — the comparison of points, rebounds, and assists to number of possessions — also leans in Westbrook’s favor.
Who knew that either of these guys were such fans of math?
At Discovery Education, we’ve been having a lot of fun writing basketball problems based on real NBA data. Check out a few problems at http://www.discoveryeducation.com/nbamath, and get a glimpse of the NBA Analysis Tool within Math Techbook^{TM} by signing up for a free 60day trial at http://www.discoveryeducation.com/math.
#mathslamdunk
Oreos, Ratios, and the Perfect Cookie
Okay, first things first. What do you call the following shape?
I call it a pill. My sons call it a racetrack. But is there a formal name for a shape formed by a rectangle with a semicircle attached to each end? If not, I feel like there should be. Place your suggestions in the Comments.
Until I hear a better suggestion, I’m gonna keep callin’ it a pill.
The following trivia question is the reason I ask.
How many pills appear around the circumference of the trademarked design on an Oreo^{®} cookie?
What’s that, you say? You didn’t know that there were little pills along the edge of each wafer on an Oreo cookie? Then you, my friend, need to pay a little more attention.
Because there aren’t just some pills around the circumference. There are 96 of those little buggers, and each of them has a rectangle with a lengthtowidth ratio of approximately 3:2 between two semicircles.
See for yourself.
Ironically, the ratio of 3:2 brings me to the main reason I’m writing today.
The original Oreo represented good design: a single layer of vanilla cream filling trapped between two crisp, chocolate wafers. But it always felt lacking to me. If only it had just a little more cream, then it would be perfect. A potential solution arrived in 1974, when Nabisco released the Double Stuf variety — two chocolate wafers with twice as much filling^{1} as its predecessor. Yet the Double Stuf teetered too far in the opposite direction. It was too sweet.
Which brings me to the delectable treat that I discovered today: the Triple Double Oreo, which is running a strong campaign for the title of World’s Best Cookie. My wife describes it as “the Big Mac of cookies.” Not two but three chocolate wafers with a thin layer of cream filling between each pair. And the pièce de résistance — one layer of vanilla cream filling, the other chocolate.
Now that’s what I call intelligent design.
It absolutely nails the ratio for wafer:filling.
Original 
Double Stuf 
Triple Double 

Wafers 
2 
2 
3 
Filling^{2} 
1 
1.86 
2 
Ratio of W:F 
2 
1.08 
1.5 
The chart above makes it all clear. The ratio is too high in the original, too low in the Double Stuf, and just right in the Triple Double. Indeed, the Triple Double Oreo is the Little Bear’s porridge of the cookie world.
This reminds me of Reese’s Peanut Butter Cups. While I haven’t quantitatively analyzed the peanut butter to chocolate ratio, qualitatively I would say that the original had a little too much peanut butter, the Big Cup was disgusting with far too much peanut butter, but nirvana was captured with the peanut butter to chocolate ratio in Miniature Reese’s Peanut Butter Cups. (Insert smacking lips sound here.)
So if you read this blog and wonder why I’m so hyper sometimes, now you know. I consume an unholy amount of refined sugar.
^{1} There is some debate about the actual amount of filling contained in a Double Stuf Oreo cookie. Although a spokesperson for Nabisco claimed that the cookies indeed contain twice as much filling as a regular Oreo, a math class in upstate New York experimentally found that Double Stuf cookies contain only 1.86 times as much cream filling as a regular Oreo. As I generally trust unpaid high school students more than moneygrubbing corporate types, I’m using 1.86.
^{2} The numbers for “filling” are relative to the amount of cream filling in a regular Oreo^{®}.
Ratio Celebration
While flipping through the Big Book of Zany Activities from Kidsbook^{®}, my sons came across the following challenge:
Can you make 25 or more words from the following word?
CELEBRATION
Alex put pencil to paper immediately and beamed as he wrote the word ratio.
It made me wonder if I could find 25 or more math words within CELEBRATION. Sure enough, I could. My list of 42 words is at the bottom of this post, though admittedly, a rather liberal view of what constitutes a math word is required, and there are even a couple of proper nouns on the list. But even removing the ones that were iffy, I think I still met the requisite number.
Speaking of ratio, you might be interested in the discussion of the No Slope… Ratio! joke. Though probably not, so here are some other ratio jokes.
A trainer at the gym was asked, “How can I calculate my body fat ratio?”
The trainer responded, “Well, if you have a body and you have fat, the ratio is 1:1. If you have two bodies, the ratio is 2:1. And so on.”Yo momma is so fat, her ratio of circumference to diameter is 4!
Math Words Within CELEBRATION:
 Abel
 Ace
 Acre
 Arc
 Bar
 Bi
 Bin
 Bit
 Caliber
 Cantor
 Cent
 Center
 Coil
 Coin
 Cone
 Election
 Eon
 Era
 Lie
 Line
 Linear
 Loci
 Lone
 Once
 One
 Orb
 Orbit
 Net
 Nil
 Rate
 Real
 Recent
 Table
 Tail
 Tare
 Teen
 Ten
 Tic
 Tie
 Tile
 Tree
 Trice