Dr. William T. Webber Whatcom Community College Bellingham, WA

Dr. William T. Webber Whatcom Community College Bellingham, WA
Six-Pin Bowling Dr. William T. Webber Whatcom Community College Bellingham, WA

Introduction Dr. William T. Webber Whatcom Community College Bellingham, WA This presentation can be found on-line at faculty.whatcom.ctc.edu/wwebber Click on the link for 6-Pin Bowling

Topics of Discussion The human pin setter.
Nomenclature for other bases. Let’s go bowling. Conclusion. The topics for talk include a brief review of how this talk and paper came about. Titled “The human Pin Setter” A nomenclature system for talking about numbers in bases other than ten. Finally some bowling activities in other bases.

The Human Pin Setter I have had the opportunity, of late, to ponder the intricacies and inconsistencies of the nomenclature for numbers in bases other than ten. You see, I have two children who love to bowl. Every week they go with their mother and grandmother to a bowling league. Mom and Gramma bowl on the league. At the end, the kids get to bowl a few frames. Back at home we have a set of toy pins and ball. So, when I come home from school my two-year old meets me at the door and says, “Daddy, me want to bowl. Me knock ‘m down, you stand ‘m back up.” How can you say “no” to that? So I gently correct his grammar, sit myself down and become a human pin-setter. He knocks ‘m down, I stand ‘m back up, all six of them

The Human Pin Setter “Me knock’m down. You stand’m back up.”
I have had the opportunity, of late, to ponder the intricacies and inconsistencies of the nomenclature for numbers in bases other than ten. You see, I have two children who love to bowl. Every week they go with their mother and grandmother to a bowling league. Mom and Gramma bowl on the league. At the end, the kids get to bowl a few frames. Back at home we have a set of toy pins and ball. So, when I come home from school my two-year old meets me at the door and says, “Daddy, me want to bowl. Me knock ‘m down, you stand ‘m back up.” How can you say “no” to that? So I gently correct his grammar, sit myself down and become a human pin-setter. He knocks ‘m down, I stand ‘m back up, all six of them

The Human Pin Setter “Me knock’m down. You stand’m back up.” Six pins.
I have had the opportunity, of late, to ponder the intricacies and inconsistencies of the nomenclature for numbers in bases other than ten. You see, I have two children who love to bowl. Every week they go with their mother and grandmother to a bowling league. Mom and Gramma bowl on the league. At the end, the kids get to bowl a few frames. Back at home we have a set of toy pins and ball. So, when I come home from school my two-year old meets me at the door and says, “Daddy, me want to bowl. Me knock ‘m down, you stand ‘m back up.” How can you say “no” to that? So I gently correct his grammar, sit myself down and become a human pin-setter. He knocks ‘m down, I stand ‘m back up, all six of them

How do we score a game? For whatever reason toy bowling sets come with only six pins. So as I sit there for hours setting pins up six at a time, I get thinking about how you might score a game of six-pin bowling. With ten pins you have ten frames per game. So, perhaps with six pins you should have six frames. And maybe, just for fun, we should keep score in base six. This turns out to be the perfect way to score. We will look at a few examples game later but first we need a good way to talk about numbers in base six.

How do we score a game? How do we talk about numbers in other bases? For whatever reason toy bowling sets come with only six pins. So as I sit there for hours setting pins up six at a time, I get thinking about how you might score a game of six-pin bowling. With ten pins you have ten frames per game. So, perhaps with six pins you should have six frames. And maybe, just for fun, we should keep score in base six. This turns out to be the perfect way to score. We will look at a few examples game later but first we need a good way to talk about numbers in base six.

A Nomenclature for Other Bases
My early misgivings The proposed nomenclature

My Early Misgivings Let’s count in base six.
From the day I started learning about other bases it has bothered me when I hear someone count in base six like this, “one, two, three, four, five, ten.” They do this because they are looking at the numerals “1, 2, 3, 4, 5, 10.” To me the word “ten” has a meaning. It is the mode of the number fingers on a pair of human hands. In base six, I propose that we use the word “six” for the numerals “10.” The following discussion usually follows when I make this proposition.

One, two, three, four, five … From the day I started learning about other bases it has bothered me when I hear someone count in base six like this, “one, two, three, four, five, ten.” They do this because they are looking at the numerals “1, 2, 3, 4, 5, 10.” To me the word “ten” has a meaning. It is the mode of the number fingers on a pair of human hands. In base six, I propose that we use the word “six” for the numerals “10.” The following discussion usually follows when I make this proposition.

One, two, three, four, five … Ten. From the day I started learning about other bases it has bothered me when I hear someone count in base six like this, “one, two, three, four, five, ten.” They do this because they are looking at the numerals “1, 2, 3, 4, 5, 10.” To me the word “ten” has a meaning. It is the mode of the number fingers on a pair of human hands. In base six, I propose that we use the word “six” for the numerals “10.” The following discussion usually follows when I make this proposition.

One, two, three, four, five … Ten. I’m sorry, but to me the word “ten” signifies the mode number of fingers on a pair of human hands. From the day I started learning about other bases it has bothered me when I hear someone count in base six like this, “one, two, three, four, five, ten.” They do this because they are looking at the numerals “1, 2, 3, 4, 5, 10.” To me the word “ten” has a meaning. It is the mode of the number fingers on a pair of human hands. In base six, I propose that we use the word “six” for the numerals “10.” The following discussion usually follows when I make this proposition.

1, 2, 3, 4, 5, 10, 11, 12 … From the day I started learning about other bases it has bothered me when I hear someone count in base six like this, “one, two, three, four, five, ten.” They do this because they are looking at the numerals “1, 2, 3, 4, 5, 10.” To me the word “ten” has a meaning. It is the mode of the number fingers on a pair of human hands. In base six, I propose that we use the word “six” for the numerals “10.” The following discussion usually follows when I make this proposition.

1, 2, 3, 4, 5, 10, 11, 12 … I want to call 10 “six.”

1, 2, 3, 4, 5, 10, 11, 12 … I want to call 10 “six.” The following conversation ensues.

They say, “But there is no ‘six’ in base six.”
So I say, “Then there should be no ‘ten’ in base ten.” Then, they say, “But ‘ten’ means one of the base.” To which I say, “Well, if I can’t use the word ‘six’ then instead of saying ‘base six’ I would have to say ‘base ten,’ where this ‘ten’ means one more than five, not one more than nine. In fact, I would never be able to tell what base I was in because I would always have to say ‘base ten.’” They say, “Oh, you are just trying to make things confusing.” No, actually I’m trying to make things less confusing. Here is the source of confusion.

My Early Misgivings Notice the difference:
There is no “six” in base six. There is no “6” in base six. There is a distinction between the word “six” and the numeral “6.” Last year our exchange student from Japan asked me if we had any symbols that represented whole words. This would be similar to Chinese or Japanese Kangi. At first I could not think of any. Then I realized that my own discipline is full o such things. Numerals are one character sybols representing entire words. In fact, in math we write complete sentences like “2 + 3 = 5

My Early Misgivings Notice the difference: 2 + 3 = 5.
There is no “six” in base six. There is no “6” in base six. 2 + 3 = 5. There is a distinction between the word “six” and the numeral “6.” Last year our exchange student from Japan asked me if we had any symbols that represented whole words. This would be similar to Chinese or Japanese Kangi. At first I could not think of any. Then I realized that my own discipline is full o such things. Numerals are one character sybols representing entire words. In fact, in math we write complete sentences like “2 + 3 = 5

My Early Misgivings Notice the difference: 2 + 3 = 5. eip + 1 = 0.
There is no “six” in base six. There is no “6” in base six. 2 + 3 = 5. eip + 1 = 0. There is a distinction between the word “six” and the numeral “6.” Last year our exchange student from Japan asked me if we had any symbols that represented whole words. This would be similar to Chinese or Japanese Kangi. At first I could not think of any. Then I realized that my own discipline is full o such things. Numerals are one character symbols representing entire words. In fact, in math we write complete sentences like “2 + 3 = 5,” or “e^(i pi) + 1 = 0.” We get so use to using these symbols as words that we forget that there is a distinction.

My Early Misgivings In base ten there is the word “ten” but not a single digit numeral for the number ten.

My Early Misgivings In base ten there is the word “ten” but not a single digit numeral for the number ten. So in base six we will use the word “six” for the numerals “10,” but we do not have a single digit numeral to represent “six.”

The Nomenclature English names for numbers.

The Nomenclature English names for numbers.
Single digit names up to twelve.

Single digit names up to twelve. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.

Single digit names up to twelve. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. Double digit names after that.

Single digit names up to twelve. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. Double digit names after that. Thirteen, fourteen, fifteen, etc.

Single digit names up to twelve. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. Double digit names after that. Thirteen, fourteen, fifteen, etc. -teen and –ty represent ten.

The Nomenclature German is the same as English.
Single digit names up to twelve. Eins, zwei, drei, vier, funf, sechs sieben, acht, neun, zehn, elf, zwolf. Double digit names after that. dreizehn, vierzehn, funfzehn, etc. -zehn and –zig represent ten.

The Nomenclature Spanish is a little different.
Single digit names up to fifteen. Uno, dos, tres, cuatro, cinco, seis, siete, ocho, nueve, diez, once, doce, trece, catorce, quince. Double digit names after that. Diez y seis, diez y siete, etc.

The Nomenclature French is a downright weird.
Single digit names up to sixteen. Un, deux, trois, quatre, cinq, six, sept, huit, neuf, dix, onze, douze, treize, quatorze, quinze, seize. Double digit names after that. dix-sept, dix-huit, dix-neuf, vingt. vingt et un, vingt-deux, vingt-trois, etc.

The Nomenclature French is a downright weird. Trouble begins at 70.

The Nomenclature French is a downright weird. Trouble begins at 70.
60 = soixant.

60 = soixant. 70 = soixant-dix.

60 = soixant. 70 = soixant-dix. 71 = soixant-onze.

The Nomenclature French is a downright weird. Then comes 80.

The Nomenclature French is a downright weird. Then comes 80.
80 = quatre-vingt.

80 = quatre-vingt. Think of Abe Lincoln. “Four score and seven years ago.”

80 = quatre-vingt. Think of Abe Lincoln. “Four score and seven years ago.” 87 = quatre-vingt-sept.

The Nomenclature French is a downright weird. Top it off with 90.

The Nomenclature French is a downright weird. Top it off with 90.
90 = quatre-vingt-dix.

90 = quatre-vingt-dix. 91 = quatre-vingt-onze.

90 = quatre-vingt-dix. 91 = quatre-vingt-onze. Clearly French is not what we will use as a model nomenclature system.

The Nomenclature Japanese is what we are looking for.
Single digit names up to ten. Ichi, ni, san, si, go, roku, sichi, hachi, ku, ju. Double digit names after that. Ju ichi, ju ni, etc. 20 is “ni ju.”

The Nomenclature Now let’s count in base six.

The Nomenclature Now let’s count in base six. 1, 2, 3, 4, 5, 10.

The Nomenclature Now let’s count in base six. 1, 2, 3, 4, 5, 10.
One, two, three, four, five, six.

One, two, three, four, five, six. 11, 12, 13, 14, 15, 20.

One, two, three, four, five, six. 11, 12, 13, 14, 15, 20. Six one, six two, six three, six four, six five, two six.

One, two, three, four, five, six. 11, 12, 13, 14, 15, 20. Six one, six two, six three, six four, six five, two six. 21, 22, 23, 24, 25, 30.

One, two, three, four, five, six. 11, 12, 13, 14, 15, 20. Six one, six two, six three, six four, six five, two six. 21, 22, 23, 24, 25, 30. Two six one, two six two, two six three, two six four, etc.

The Nomenclature What about larger numbers?

The Nomenclature What about larger numbers?
Let’s model large numbers after American English numbers. 100

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000 is “sixcube.” 10,000

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000 is “sixcube.” 10,000 is “six sixcube.” 100,000

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000 is “sixcube.” 10,000 is “six sixcube.” 100,000 is “sixsquare sixcube.” 1,000,000

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000 is “sixcube.” 10,000 is “six sixcube.” 100,000 is “sixsquare sixcube.” 1,000,000 is “sixmil.” 1,000,000,000

Let’s model large numbers after American English numbers. 100 is “sixsquare.” 1000 is “sixcube.” 10,000 is “six sixcube.” 100,000 is “sixsquare sixcube.” 1,000,000 is “sixmil.” 1,000,000,000 is “sixbil.”

The Nomenclature Pop quiz.

The Nomenclature Pop quiz.
Write the name of the following base six number.

Write the name of the following base six number. 23,512,432.

Write the name of the following base six number. 23,512,432. Two six three sixmil five sixsquare six two sixcube four sixsquare three six two.

Write the name of the following base seven number.

Write the name of the following base seven number. 23,512,432.

Write the name of the following base seven number. 23,512,432. Two seven three sevenmil five sevensquare seven two sevencube four sevensquare three seven two.

The Nomenclature Notice the two answers. 23,512,432.
Two six three sixmil five sixsquare six two sixcube four sixsquare three six two. Two seven three sevenmil five sevensquare seven two sevencube four sevensquare three seven two.

The Nomenclature If we didn’t know what base. 23,512,432.
Two base three basemil five basesquare base two basecube four basesquare three base two.

Write the numerals that represent the following base six number.

Write the numerals that represent the following base six number. Four sixsquare three six sixbil two six five sixcube sixsquare six.

Write the numerals that represent the following base six number. Four sixsquare three six sixbil two six five sixcube sixsquare six. 430,000,025,110.

Let’s Go Bowling Sample games. You keep score.

Let’s Go Bowling Here are the rules.

Let’s Go Bowling Here are the rules.
Adults bowl with ten pins for ten frames, score is kept in base ten.

Adults bowl with ten pins for ten frames, score is kept in base ten. Kids bowl with six pins for six frames, score is kept in base six.

Adults bowl with ten pins for ten frames, score is kept in base ten. Kids bowl with six pins for six frames, score is kept in base six. Gramma, Mom, Kirsten and Willie play a round-robin tournament.

Adults bowl with ten pins for ten frames, score is kept in base ten. Kids bowl with six pins for six frames, score is kept in base six. Gramma, Mom, Kirsten and Willie play a round-robin tournament. Dad keeps score.

Adults bowl with ten pins for ten frames, score is kept in base ten. Kids bowl with six pins for six frames, score is kept in base six. Gramma, Mom, Kirsten and Willie play a round-robin tournament. Dad keeps score. Papa can’t understand why Dad gets so excited about all this.

Let’s Go Bowling Game 1. 1 2 3 4 5 6 7 8 9 10 - Mom 18 27 36 45 54 63
72 81 90 1 2 3 4 5 10 - Kirsten 14 23 32 41 50

Let’s Go Bowling Game 1. Mom is ten pins short of one hundred.
Kirsten is six pins short of one sixsquare. Both are 10 short of 100. Tie game.

Let’s Go Bowling Game 2. 1 2 3 4 5 6 7 8 9 10 / Gramma 11 22 33 44 55 66 77 88 99 110 1 2 3 4 5 10 / Willie 11 22 33 44 55 110

Let’s Go Bowling Game 2. Gramma is ten pins over one hundred.
Willie is six pins over one sixsquare. Both are 10 pins over 100. Tie game.

Let’s Go Bowling Game 3. 1 2 3 4 5 6 7 8 9 10 / Gramma 19 38 57 76 95 114 133 152 171 190 1 2 3 4 5 10 / Kirsten 15 34 53 112 131 150

Let’s Go Bowling Game 3. Gramma is ten pins short of two hundred.
Kirsten is six pins short of two sixsquare. Both are 10 pins short of 200. Tie game.

Let’s Go Bowling Game 4. 1 2 3 4 5 6 7 8 9 10 X Mom 30 60 90 300 1 2 3
120 150 180 210 240 270 300 1 2 3 4 5 10 X Willie 30 100 130 200 230 300

Let’s Go Bowling Game 4. Wow! Two perfect games. Tie game.

Let’s Go Bowling Your turn to keep score. 1 2 3 4 5 10 X / Dad 1 2 3 4
Papa

Let’s Go Bowling Your turn to keep score. 1 2 3 4 5 10 X / Dad 20 1 2
Papa

Let’s Go Bowling Your turn to keep score. 1 2 3 4 5 10 X / Dad 20 34 1
Papa

Let’s Go Bowling Your turn to keep score. 1 2 3 4 5 10 X / Dad 20 34
43 1 2 3 4 5 10 X / Papa

43 101 1 2 3 4 5 10 X / Papa

43 101 121 1 2 3 4 5 10 X / Papa

43 101 121 151 1 2 3 4 5 10 X / Papa

43 101 121 151 1 2 3 4 5 10 X / Papa 25

43 101 121 151 1 2 3 4 5 10 X / Papa 25 44

43 101 121 151 1 2 3 4 5 10 X / Papa 25 44 104

43 101 121 151 1 2 3 4 5 10 X / Papa 25 44 104 124

43 101 121 151 1 2 3 4 5 10 X / Papa 25 44 104 124 143

Conclusion What is the the significance?

Conclusion What is the the significance? Use as an in-class activity.

Conclusion What is the the significance? Use as an in-class activity.
Talk about numbers in other bases without the confusion of base ten names.

Talk about numbers in other bases without the confusion of base ten names. Can easily use any triangular number to bowl with.

Talk about numbers in other bases without the confusion of base ten names. Can easily use any triangular number to bowl with. Could make a new handicap system for bowling.

Six-pin Bowling Dr. William T. Webber Whatcom Community College
Bellingham, WA This presentation and paper are available at: faculty.whatcom.ctc.edu/wwebber

Dr. William T. Webber Whatcom Community College Bellingham, WA

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