A hammer and a nail

Panacea was a goddess of healing in Greek mythology. She was thought to carry a potion that would heal any sickness. Her name evolved into an English term for a drug to cure all diseases. In addition, Panacea may have led us to the hammer and nail theory:
 
In 1964 Abraham Kaplan said, "I call it the law of the instrument, formulated as follows: Give a small boy a hammer, and he will find that everything he encounters needs pounding."

In 1966 Abraham Maslow revised this, saying, "It is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail."

Common usage simplified this to: "If you only have a hammer, everything looks like a nail."

We eventually arrived at the software programmer's notion of the golden hammer - the hope that if we are lucky, a single, familiar technique solve virtually all software problems.

Apparently the term "when all you have is a hammer" has become the golden hammer for journalists, as it received 15.7 million hits when I searched for it today. It's a great blog title.

So why do I raise my hammer in the math blog? Because I read yesterday:

The reason you have to learn math is to solve problems when you grow up.

This author is implying Math is a golden hammer. Math is a panacea.

I'm sorry, but I disagree. Math is not a cure for all that ails us. Math is helpful if the world around you is filled with math-resolvable problems - but most problems aren't solvable with math, and math is good for a lot more than just problem-solving.

Two years ago I wrote, If language is a system for encoding and decoding information so it can be shared, then math indeed can be a language. A language of counting, measurement, shapes and calculation. A language with precise definitions and specialized terms.

You learn math to talk to other people about money, or brag about your batting average or mention your low score on this weekend's round of golf or the high mileage you just achieved with your new hybrid car. Those aren't problems, they're opportunities. Please allow me to rephrase the statement:

The reason you have to learn math is to communicate about many things that are important to you.

Okay. Now we can get to the interesting part - what is a hammer?

A hammer is a hand tool meant to deliver a concentrated impact to an object. The most common uses are for driving nails, shaping metal and breaking objects. Hammers are designed for specific purposes. Although they vary widely in shape and construction, most hammers have a handle and a head, with the weight concentrated at the head. 

And why do you need one?

• driving nails into wood and/or removing nails (claw hammer)
• quieting a noisy courtroom (gavel)
• shaping metal (ball peen hammer)
• breaking rocks or concrete (sledgehammer)
• climbing up a wall of snow (ice hammer)
• tightening a wheel retaining nut (lead hammer)
• hitting an enemy on the head (war hammer)
• putting tacks into furniture upholstery (tack hammer)
• installing small watch parts (tap hammer)
• finishing jewelry (chasing hammer)
• removing dents from soft metal (mallet)

Notice there was only one mention of nails in this list. Although they are indeed very useful tools, hammers aren't a panacea for all that's ailing around us. And neither is math.

Math Secrets in Sports: Pitching Horseshoes

This week in the Excel Math Blog we are revealing inside mathematical secrets of popular, challenging-to-score sports. After dealing with tennis, bowling, and archery we have come to pitching horseshoes. If you participate in this activity, you will need to learn the rules and you may have to brush up on the math you learned in elementary school (possibly using our Excel Math curriculum).

Have you ever just barely missed a goal, a basket, or sinking a putt? You spun around in reaction, shouting "but I was so close!" And some wiseguy said, "Close only counts in horseshoes and hand grenades!" If so, here's your chance to find out what they mean - for in very few sports do you get a score for missing the target.

Horseshoes is an activity where 2 competitors on a 50-foot court pitch (throw) horseshoes at a 14 inch-tall metal stake 40 feet away in the middle of a sand pit. Here's a diagram:

Horseshoe events are divided into innings. Typically, 4 horseshoes are thrown per inning, 2 by each competitor. Both of your shoes must be thrown within 30 seconds, using the same hand. In most games, the person whose shoes are closest to the stake scores, and the other player gets no score in that inning.

Pitched shoes 
After all shoes in an inning are pitched, they are ruled either live shoes or dead shoes. A live shoe has been legally thrown and ended up in the pit area. A dead shoe was thrown illegally and/or ended up outside the pit, or was cancelled by an opponent's ringer.

Ringers
A ringer is a live shoe circling the stake. A straightedge across the open end of the shoe must not touch the stake in order for it to be ruled a ringer. A ringer is worth 3 points.

Leaners or Close 
A live shoe that is not a ringer, but is resting 6 inches or closer to the stake (including leaning on the stake) has a value of 1 point.

Out of Count
A shoe resting more than 6 inches from the stake is out of count and has no value. A foul or dead shoe is out of count, no matter where it comes to rest. Foul or dead shoes should be removed before the next shoe is thrown. These infractions cause a foul shoe:

• stepping over the line while throwing
• not throwing within the time limit
• throwing with the opposite arm
• hitting an fixed object outside the court like fence, post, etc.
• a shoe that breaks when hitting the stake is a foul
• a shoe broken by another shoe striking it is not a foul and is scored where it lies 
• a shoe hitting a moving object (falling leaves, person, etc.) is not a foul and can be rethrown

Equipment
Horseshoes are normally made of forged or cast steel or iron, and must weigh no more than 40 ounces (1134gm). The opening may not be wider than 3 1/2 inches. They are thrown so they rotate in flight. Here's a site with a wide selection or horseshoes.

Players can buy special tools to remove sharp edges from horseshoes, to verify ringers, to lift mucky shoes, and to measure the distance from the stake.

Associations
If you like horseshoes, you may want to visit the National Horseshoe Pitcher's Association website. The 2011 World Championships will be held in Monroe, LA next week.

NHPA claims that around 15 million enthusiasts in North America are pitching horseshoes, because it's one of a few inexpensive, back-yard-friendly sporting activities.

Competitors
A couple years ago, Alan Francis from Ohio went 19-0 in the championship horseshoe finals, setting a world record of 917 ringers out of 1,016 shoes pitched! Alan has won the world championships 16 times, and as of this week, is hitting 90% ringers in competition!  You can look at his recent scores here.

Joan Elmore from Tennessee has been the ladies champion 4 times, and is throwing about 84% this year.

Competition averages are calculated like this: Total ringers pitched are divided by total shoes pitched and the result is multiplied by 100 and calculated to 2 places past the decimal point (not rounded off like I did above).

Math Secrets in Sports: Archery

This week in the Excel Math Blog we reveal a few of the inside mathematical secrets of popular sports. After dealing with tennis and bowling, we've come to Archery. If you take up this activity, you may have to learn new math or relearn the old math you learned in elementary school (possibly with our Excel Math curriculum).

In archery you need to understand distances, weight, straightness, keep track of time, learn to wait your turn, and add numbers rapidly and accurately. And count your pennies!

In some ways, archery sounds easy, doesn't it? No running. No tackling. You pull a string, shoot an arrow, hit a target. But it's not so easy. You need calm nerves, strength, speed, good eyesight, ability to repeat the same motion over and over and over ...

On Father's Day, I watched my brother-in-law explaining archery technique to my nephew.

To avoid any problems, he was pretty close to the hunting target, that square black box back by the horse barn. The horses were elsewhere, for safety.

I'll review a bit of the math details of archery. Some details will vary depending on whether you are doing target archery or field archery (hunting).

ARCHERY
LEAGUE - a seasonal group of meetings where many archers and teams can shoot
   TOURNAMENT - a competition with many archers or teams shooting to win
      ROUNDS - this term describes shooting a batch of 2 to 6 dozen arrows for each target distance in competition
       ENDS - an end is a 2-minute interval time, during which an archer must shoot a group of 3 or 6 arrows, after which they are scored and retrieved. There are often 20 ends in a round
         POINTS - scores depend on where the arrows hit within 10 evenly-spaced concentric rings. The values range from 1 to 10 increasing towards the center (these values may vary from country to country). Some have an inner 10 ring:

• 1 ring and 2 ring - white
• 3 ring and 4 ring - black
• 5 ring and 6 ring - blue
• 7 ring and 8 ring - red
• 9 ring, 10 ring and inner 10 ring - gold

After each end, archers add the scores for their arrows - if an arrow touches a line, you can claim the higher value. Scores for each arrow in an end are written in descending order on the score card (10, 9, 4, 4, 3, 3). No one may touch the arrows until the scoring is complete, in case a referee wants to inspect one. If you count wrong and shoot too many arrows, the highest scoring arrows are subtracted from your score.

Target sizes and distances vary, depending on the competition:

• 16 inch (40cm) for 60 feet (18m) indoors
• 24 inch (60cm) for 80 feet (25m) indoors
• 32 inch (80cm) for 100 feet (30m) and 160 feet (50m)
• 48 inch (122cm) for 240 feet (70m) and 300 feet (90m)
• All target backings must be at least 48 inches round or square, regardless of target size
• The center of the gold must be 51 inches (130cm) above the ground +/- 2 inches (5cm)
• Targets must slope backwards, within 10-15° from vertical

Arrows

• Arrows range from 26-31 inches in length, measured from the bottom of the nock on the back to the front (not including the tip) and must be less than .27 inches (9.3mm) in diameter; good arrows are within +/- .001-.006" in straightness
• Arrow weight is measured in grains (1/7000th of a pound); most weigh between 200 to 400 grains - you might have 5 grains weight of arrow per pound of draw on the bow
• Arrows travel at speeds from 200 to 300 feet per second (fps) and so they reach a 160 foot (50m) target in about half a second (you can do the math)

Here's an on-line course on arrows, with lots of math details, charts and diagrams.

Bows

• Bows are made of different kinds of materials and may have sights, but must have no electronic features
• The power of a bow is expressed in pounds of draw weight or effort it takes to pull the string back
• Both compound and recurve bows are used, but not mixed in the same events

Scoring is done in different ways; in target archery many countries follow FITA rules:

• The top archery score in FITA competition is 1440
• Archer Brady Ellison recently shot a 1368 score in competition - the highest recorded score in competition by a non-Korean archer.
• Koreans dominate archery with 90% of the world records. They have used bows and arrows since before recorded history. Korean archers aggressively pursue excellence in competition - some shoot over 1000 arrows a day, 6 days a week!

If only we all were so diligent in learning math!

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Math Secrets in Sports: Bowling

Hello again. This week in the Excel Math Blog we reveal the shocking inside mathematical secrets of sports!

Today we investigate 10-pin Bowling (because 100 million people around the world participate). Bowling, like the other spots we're discussing, will force you to learn new math or relearn the old math you learned in elementary school (or you could rely on the bowling computer).

In Bowling you count up pins you knock down, you carry-over certain scores, you adjust your actions based on the if you get 2 strikes you throw again rules, and so on. If you bowl in a league you will soon get a handicap (not a disability, but an adjustment to your score).

I'll just give a brief overview of the math and terms used in Bowling:

BOWLING
LEAGUE - a competition over a period of months where teams of bowlers compete
TOURNAMENT - a short-term competition with many bowlers or teams competing to win
   SERIES - a team must win 2 out of 3 games to win a series (usually the team members' scores are added to get a team score)
      GAME - a player needs the highest score to win a game. The most you can score is 300
         FRAME - players don't win individual frames; the best score on 10 frames wins a game
            POINTS - the various combinations are decided by how many pins are knocked down, and when they fell:

• strike (10 pins with 1 ball)
• spare (10 pins with 2 balls
• open (less than 10 pins with 2 balls)

To learn more, click here.  To view a Bowling Score App for your iPhone, click here. This is what a typical scoring screen on the App looks like:

Bowling is usually done with groups of people so it's more fun if you have two lanes rather than one. A single bowling lane is shown below (not to scale):

If you ever dreamed of having your own bowling alley at home, you will need about $100,000 or so. Lanes are made of wood or synthetic materials. The rules declare:

• Each lane is 62 feet 10 and 3/16ths inches from foul line to the pit where the pins fall
• It's 60 feet from the foul line to the center of the No. 1 pin spot (plus or minus 1/2 inch)
• It's 2 feet 10 and 3/16ths inches from the center of the No. 1 pin spot to the pit
• Each lane must be between 41 and 42 inches wide
• The total width of a lane with gutters must be between 60 inches and 60 and 1/4 inches wide
• The lane must be free of grooves, with no more than 40/1000th inch variation in level and/or dents (smoothness)
• You need a room 90-100 feet in length, 15 feet in width and 12 feet in height to have a pair of bowling lanes
• Lanes sit about 16 inches above your foundation because the balls come back under the lanes
• The pins are 15 inches tall and 4.7 inches wide; weigh between 3 pounds 6 ounces and 3 pounds 10 ounces
• The ball must be less than 27 inches in circumference, cannot weigh more than 16 pounds and can contain no metal whatsoever (if you need one, go here, they have 1800+ different bowling balls to choose from!)

Math Secrets in Sports: Tennis

Just when kids think they are getting the hang of math, (one, two, three - the higher you go the more value you have) they have to leave the comfort of the classroom and march out into the harsh sunlight on the playing field. There, in sometimes traumatic circumstances, they discover that the math they learned in the classroom is not enough to deal with sports!

This week in the Excel Math Blog we reveal the shocking inside mathematical secrets of  sports! Today we expose Tennis (because Wimbledon is just over) and tomorrow we will investigate Bowling (because so many millions of people participate). In each of these sports you have to learn new math or relearn your old math.

In Tennis you do more than count runs or hits or baskets or goals. You count up using new names for numbers, then count back, adjust your actions to suit the win by at least 2 points contingency rules, and so on.

I'll just give a brief overview of the math and terms used in Tennis:

TENNIS
TOURNAMENT - a competition where lots of tennis players compete to find the overall winner
   MATCH - a player needs to win 2 out of 3 (or 3 out of 5) sets to win a match
      SET - a player needs to win 6 games (and at least 2 more games than the opponent) to win a set
         GAME - a player needs 4 points (and at least 2 more points than the opponent) to win a game
            POINTS - the points are called:

• Love = 0
• First point = 15
• Second point = 30
• Third point = 40
• If both have 40 it's called deuce
• there's another term called advantage

To learn more about tennis math, click here.  If you want to provide input on an App for tennis, fill out a survey here.

A tennis court is shown below. It can be surfaced with clay, grass, wood or asphalt or other hard materials. A hard surface court will cost about $25-30,000 to build.

A tennis court is 27 feet (singles) or 36 feet (doubles) wide and 78 feet long. The net is 3 feet 6 inches high at the ends, and can droop to 3 feet in the middle. Poles for the net are set 3 feet outside the doubles lines, so the net is 42 feet long [36 + 3 + 3 = 42] .

The court should be level with just enough slope for water to run off (a maximum of 1 inch in 10 feet of distance).

To avoid the players running into fences or stands, the court needs extra space around it - about 12 feet on each side and 21 feet at each end. To keep from losing tennis balls, and for safety, courts are usually surrounded by 10-foot chain-link fences.

You can buy a fence "kit" with all you need to enclose a pair of courts, for about $12,000. That's 120 feet long, 120 feet wide, and 10 feet high with 2 gates. Wind screens for the fence cost an additional $1000 or so.

Garbage Truck Math, Part II

After yesterday's blog about garbage trucks, I got feedback that folks really enjoyed the post. So I decided to do another one on garbage trucks.

Many kids love garbage trucks. Why? My wife told me how her kids on the playground stop and run over to watch the garbage trucks pick up bins at the school. Why are so many kids (and grown-ups) fascinated with garbage trucks?

I decided to research this a bit, and saw this quote today:

Just as toddlers are fascinated with how their bodies work, they often love machines ... The garbage truck is a great big, loud machine. It has moving parts that go up and down and it seems big and strong. The trash collectors are big and strong too, able to drive those trucks and make the grinders work. Kids want to be like the grownups - those guys control machines even bigger than they are! My kids even learned the days of the week so they could anticipate when it was garbage day and be sure to be outside in time to see the truck come.

What age group likes watching garbage trucks? I scanned a few videos on YouTube, and noticed some comments. These are arranged in order from lowest age to highest:

• If you have a toddler, then you know your local garbage man is like a rock star!
• My son has been obsessed with this video for a week... every morning he points to the computer he is not even 2!!!!
• Since I showed my 22-month-old nephew this video, every time I'm on a computer he comes over saying "trassssh truck" ... he loves it and dances to the music.
• This is my 2 year old son's favorite video. He watches it every day!
• My 3 year old son is fascinated with garbage trucks. He can see the apartment building dumpster through his bedroom window - when he hears the garbage truck pull up he races to his window to watch.
• My 3 year old stepson thought this was great (so did my 16 year old friend - he too loves this)
• I guess this is a phase my little one is going through for the 3yrs of living life on this lovely earth.  I admit after the zillon time watching the same video it's not bad.
• Our 4 year old loves this so much and we thank you very much for posting it.....
• My nephew JD has to watch this video 10 times daily  (We all enjoy it)
• What is it about trash trucks???? My kid loves this! "Daddy I want see trash truck" over 'n over again.
• Trash trucks appeal to all the senses...you can see them, smell them, touch them, hear them! They have moving parts, big sounds! I just love them ... they bring out the child in me!

Adults watch garbage trucks even if they don't love them Researchers in Chicago studied garbage collection - but not because the drivers are "rock stars." They want to operate the trucks more efficiently. Here's a study of their report:

We investigated garbage trucks in Chicago. Our analysis showed that city blocks differ in the rate at which garbage accumulates. Formerly, each truck visited the dump twice a day regardless of load. We devised flexible routing so some trucks go to the dump once a day, while others go twice. We use a Markov decision process to model the impact of flexible routes. This dynamic scheduling algorithm adjusts the number of dumpsite visits throughout the week to maximize service, which means we could reduce trucks by 12-16% - a significant savings. In addition, we created a "night shuttle" program. Garbage trucks used to leave early to go dump their loads and get back to their assigned yards by the end of each shift. Truck crews now remain on their routes and leave the trucks fully loaded at the end of the day. The trucks are shuttled to their dump sites, emptied, and returned by a crew of second‑shift drivers.

What does a garbage truck driver do all day? (Math, but fun) Starts at 6 am and drives for 8-10 hours over a 45-60 mile route, stops at 500-800 homes, handles a truck that can hold 16,000 pounds of garbage and goes to empty his truck twice a day. Top speed of a garbage truck is around 55 mph, but they rarely go faster than 15 mph. Would you like to ride along? Have a virtual ride first:



Garbage Truck Math Game  Plot the most efficient route for your garbage man. Count the number of homes and decide if this can be done in one day. Then if possible, with no back-tracking, no left turns, no backing up and no wasted time, design a route. Here's an example of what I mean [click image for a larger version]:

Now for a real challenge. Below you can see a city map. Alleys are shown with dotted lines. The 997 houses are shown by numbers on each block. Divide the route into two equal halves with a minimum of backing up and left turns. Click on the map below [to enlarge it], print it out, and start plotting!

(Yes, I know this is what we have computers do for us - but who is going to program the computers? If you are good at this, you've got a job awaiting!)