Last week, in Number Sense 039, Awkward Goat and Billy Goat Gruff explored Fibonacci series using Leonardo of Pisa's classic rabbit reproduction puzzle. They decided sauce for the goose wouldn't really work for the gander, besides, metaphors involving cooking farm animals left them feeling a bit queasy.

This week finds them wandering in a circle around a tree...

“What on earth are we doing, Awkward Goat?” asked Billy Goat Gruff.

“Why, we are walking around a tree,” replied Awkward Goat.

“Yes, yes, but why are we walking around a tree?”

“Let's suppose...” began Awkward Goat.

“Not this again!” said Billy Goat Gruff.

“...that we are walking along a number line,” continued Awkward Goat, undeterred by Billy Goat Gruff's bad attitude.

“And let us imagine a fence around the tree, with equally spaced fence posts.”

“Of course,” replied Billy Goat Gruff, “I see them now!”

“Well, then,” asked Awkward Goat, “how many are there?”

“Let's suppose,” said Billy Goat Gruff, “that there are twelve of them.”

“Oh very good,” replied Awkward Goat. “Let's number them.”

“Fine. This is number one, this is number two...”

“Wait! Have you forgotten this is a number line? What number do we start with on a number line?” asked Awkward Goat.

“Sorry, I didn't realize it was so important,” replied Billy Goat Gruff. “We start numbering with zero, so this is number Zero, this is number One, this is number Two, this is number Three...”

Billy Goat Gruff stopped abruptly.

“What's the matter?” asked Awkward Goat.

“That post already has a number,” replied Billy Goat Gruff. “What do we do now?”

“Since our circular number line has a fixed length,” replied Awkward Goat, “we are finished numbering the posts. It's not like an ordinary number line which goes on forever in both directions. We can call it a number circle.”

“But what good is it?” asked Billy Goat Gruff. “I can use an ordinary number line for addition and subtraction and multiplication. This circular number line doesn't even have negative numbers!”

“That's true,” said Awkward Goat, “and it seems we don't need them. If we turn around and walk the other way, which can be considered going in the negative direction, we will always get to some numbered post, which is the answer to any subtraction problem.”

“So if we go forward, say, to two, then subtract a larger number, say four, by going the other way, we would ordinarily get a negative number. Two minus four is negative two. But on this circular number line we get ten! How on earth does that make sense?” asked Billy Goat Gruff.

“What time is it?” asked Awkward Goat.

“Don't dodge the issue,” said Billy Goat Gruff. “Answer my question.”

“Humor me,” Awkward Goat requested.

“All right. It's two o'clock,” replied Billy Goat Gruff.

“And we've been walking around this tree for how long?”

“Four bloody hours!” answered Billy Goat Gruff, “more or less.”

“And that means we got here...” began Awkward Goat.

“At ten o'clock this morning!” finished Billy Goat Gruff.

“So two o'clock minus four hours is...”

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#### Comment Preferences

• ##### Tips for zero hour(10+ / 0-)

time to launch something!

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

• ##### ...about those goats and a tree...(7+ / 0-)

I love nature, science and my dogs.

• ##### ROFLMAO(6+ / 0-)

Thanks for that, Polly! :)

Good thing my goats imagined that fence...

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### Good post and my guess is that there may be 60(6+ / 0-)

By the way, I am following you now.  In fact, I noticed there are over 150 people following you.  Don't feel paranoid though.  I'm sure it's just that we just like your posts.

"Individual commitment to a group effort - that is what makes a team work, a company work, a society work, a civilization work." - Vince Lombardi

• ##### Really, I don't feel stalked at all(5+ / 0-)

Welcome to my little corner of the mathematical world. The leading zero does indeed give the series room to grow. And
Billy Goat Gruff does a remarkable job keeping the trolls away (we only had one, and he hasn't been seen for quite a while.)

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### utterly brilliant method you have here. (4+ / 0-)
Recommended by:
Orinoco, Polly Syllabic, Quequeg, palantir

Take concepts in math that are abstract, represent them visually, and have a couple of cute critters to enable folks to put themselves in the picture.

Perfect.

We don't all have to be mathematicians to become math-literate, nor do we have to be scientists to become science-literate.  The key is having enough conceptual knowledge to be able to function in the civic realm, and also to know where to look and who to ask for additional information.

"Minus two votes for the Democrat" equals "plus one vote for the Republican." Arithmetic doesn't care about your feelings.

[ Parent ]

• ##### We all know more than we think we do(4+ / 0-)
Recommended by:
G2geek, Polly Syllabic, Quequeg, palantir

if we take the time to stop and think about it.

Math has such an interesting relationship to reality, that math can also be considered to have a liberal bias. Becoming math literate means you're able to figure things out for yourself. Once that starts, there's no turning back. ;^)

And, I like goats.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### because if you can't be a hip cat(4+ / 0-)
Recommended by:
Polly Syllabic, G2geek, Orinoco, palantir

be a mod(Goat).

Charming as always.  They look so cute, every week...

...j'ai découvert que tout le malheur des hommes vient d'une seule chose, qui est de ne savoir pas demeurer en repos dans une chambre.

• ##### Awkward Goat is very hip(3+ / 0-)
Recommended by:
jessical, Polly Syllabic, palantir

he's just not a cat.

Damn me if these two aren't taking on their own personalities and starting to drive the narrative.

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### That's funny...(3+ / 0-)
Recommended by:
Polly Syllabic, Orinoco, palantir

...because as I read this one, I imagined Lewis Caroll starting to write about the absurdity of symbolic algebra and ending up through the looking glass :}  Not in tone but definitely in the sense these goats have a certain...narrative profluence.:}  You want to know what happens next with the goats!

...j'ai découvert que tout le malheur des hommes vient d'une seule chose, qui est de ne savoir pas demeurer en repos dans une chambre.

[ Parent ]

• ##### If my grin on reading this gets any wider(3+ / 0-)
Recommended by:
jessical, Polly Syllabic, palantir

I will start to disappear, just like the Cheshire Cat. I am overjoyed you want to know what happens next with the goats. That touches me deep in my storytelling soul.

(Although I in no way aspire to the mantle of Lewis Caroll...)

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]

• ##### Recc'ed for those ever-lovin'(3+ / 0-)
Recommended by:
Polly Syllabic, Orinoco, palantir

goats.  And, oh yes, the math concepts.

• ##### Awkward Goat says "Hi!"(2+ / 0-)
Recommended by:
Polly Syllabic, palantir

and so does Billy Goat Gruff. ;^)

"The problems of incompetent, corrupt, corporatist government are incompetence, corruption and corporatism, not government." Jerome a Paris

[ Parent ]