Links:

Falling Sand Game
Online whiteboard
Indexed diagram
Knot theory and practice too!
The Fib
Definition wars


The Fibonacci Wall, a decoration of a building in Gothenburg, Sweden. Photo by Eva the Weaver - also check out her Mathematics on the Loose photo collection!

We had a fantastic meeting on Monday. About twenty people participated. A day later, I am still jazzed up from all the wonderful mathematics everybody created there. But first things first! Most club members accepted several small quests throughout the meeting, and here they are all together. I am copying the quests at the end of this email, too, after the stories.

We started the club from a name activity I call Zany Stars. It is inspired by diagrams from the Indexed blog. You make up a word starting from every letter of your name, choosing words that mean something to you. Club members chose names of their pets, things they liked to do, or funny silly ideas. Then you make a polygon with as many corners as there are letters of your name. Finally, you connect letters by two, and use the creative side of your brain to figure out what these words can possibly mean, put together! Here are a few examples from the meeting, and I hope club members will scan and upload their pictures very soon so that there are illustrations, too! There was so much creativity about combining ideas.

ETHAN
E=eat
T=trucks
ET=ice cream truck

ANNE
A=arts
N=nuts
AN=zany
(This gave me the idea for the name of this game - MariaD)

KELLEY
E=ecstatic
Y=yours truly
EY=I am ecstatic about my book

CAITLIN
C=cat
A=angel
CA=flying cat

MICHAEL
H=help
L=light
HL=window (it helps with lighting)

COLE
C=creation
O=outdoors
CO=nature creations, like something made out of leaves

DARLENE
L=light
E=eating
LE=diet

CHLOE
E=eating
L=library
EL=cookbook

CALVIN
V=victory
I=ice cream
VI=sweet victory

ZANE
N=nuts
Z=zoo
ZN=monkey

ZAKARY
A=animals
R=running
AR=cheetah
The mathematical underpinnings have to do with combinatorics. How many pairs can you make out of the letters of your name? We will explore this question more at the next meeting! Combining unlikely things and figuring out what they mean together is one of the most powerful brainstorming techniques. Many meditation and creativity systems use it, from the ancient Chinese I Ching philosophical tools to the modern De Bono's management workshops.

Then we went outside and played a rhythm game about names. Throw a giant ball around, and when you catch it, you say your name and everybody repeats it twice. It is more fun than the description. But then we played a game called "Human Knots": come together, grab random hands, and then try to untangle the resulting mess! The game helps with learning names, too, because everybody gives each other directions, or else yells for help when the tangle becomes too much. Our knot untangled into two loops, but sometimes there is one loop or more. Here is a knot theory site with pictures and more activities.

We took a snack break and then started another word activity, suggested by Elizabeth R.: "My Sequence Poems." We looked at an example of a sequence created by an Italian mathematician named Fibonacci. It starts with 1 and 1, and then adds the previous two numbers to get the next, so it goes 1, 1, 2, 3, 5, 8, 13... A poem based on that sequence has as many syllables in each line. Club members created their own sequences, named them - sometimes with their own names, like that Fibonacci guy, and sometimes with pet names - and then made poems in their sequence's meter. An interesting example: Darlene S. created a sequence that started with 2, 2 and then added numbers, that is, it had the same rule as Fibonacci. You can draw a beautiful spiral based on the Fibonacci sequence, and this spiral is everywhere in nature - shells, leaves, fruit and so on. You can see some pictures in Wikipedia, for example. Darlene's sequence forms a spiral of the same shape, but twice as large. This is an excellent good visual example of a proportion based on 1:2 ratio. I think I will use it with my students to introduce ratio and proportion. Here are a few examples of sequences and poems people created:

Kelley Sequence
1,3,5,7,9
Peace
Gazing up into
The big, cloudy sky
Feeling the grass beneath me
I'm drifting off into peaceful bliss

Tash Sequence
X+X+X-X-X
X=2
2 hi there!
4 My name is Tash
6 I am a collie dog
4 do you have food?
2 munch, munch

Acorn Sequence
2, 2, 4, 6, 10
Acorn
is fun.
He likes to play.
He is a flying squirrel.
He is cute and likes to be held gently.

Sally Sequence
2, 4, 6, 10
my cat
ate so much food
he gets so fat sometimes
he comes to me and meows for his food

Cait's sequence
3, 4, 6, 8
a towcan
a towcan's love
a towcan's love is may
a towcan's love is may from sky

From profound to funky, poems were excellent. Even non-poets can create something interesting given a form, and sequences help us create forms and patterns. Michael S. wrote an involved story based on his sequence - it was too long for me to retype during the club, but hopefully he will upload it to the forum in the next few days and we can all read it together. Both Zany Stars and My Sequence Poem are example of "collection" or "collage" activities, where everybody uses a similar frame, but creates his or her own unique object to contribute to the collection. Creating a collection is one surefire way of bringing a multi-age, multi-level group of people together in one meaningful endeavor. The math jokes people brought and shared is another example of a "collection" activity. These activities are divergent and creative, and build pleasant, warm feelings of everybody being included and appreciated.

Not so with Definition Wars! The goal of the activity is to create one single definition per group. Of course this goal produces conflicts. Whose ideas will be included? Which train of thought will the group pursue? Who will speak next? What a strife! Lucy L. suggested we use a talking stick to deal with taking turns. The way the Definition Wars go, somebody proposes a definition and the next person can say "Objection!" if they have a counterexample, something that should have been included, or other correction. The next person fixes the definition based on objections, and the game continues. My favorite part is the discussions of particular juicy objections - for example, what came up in trying to define "Number": "Does the number line start from zero?" or "Are words a type of symbols?" The activity is too rough right now, but I don't want to give up on it. One of the quests today is to fix it.

Speaking of fixing things, I need to bring many more things for people to quietly handle when they are taking breaks or just talking. Next time, I will have modeling clay, pipe cleaners, legos, yarn and such so that people can get their sensory integration covered better! A word about a few younger kids we had: they are able to participate in every single activity, but two and a half hours is a long time to stay focused. I think it is prudent to expect people to disengage sometimes. It is ok for them to go to the kitchen and snack, or play with a construction set there. They can hear everything anyway. I loved how Zane S. was playing with a magnet toy on the floor during a Definition War about squares, making illustrations - squares, cubes, what not, while not directly creating definitions or objections - it was a valuable contribution. This is called "peripheral participation" and it is very appropriate, especially for younger club members.

If you are one of the families who missed the club because of an illness, you can come on Wednesday at 9:30 or Friday at 10 - we will have similar activities. You can also still do the quests at home. I want to thank the good elves who cleaned the kitchen, folded all the chairs and in general made the rooms look neat after the club. I did not see who it was - the rooms were just magically clean afterward - and it helps a lot!

I am looking forward to meeting you in two weeks, on Monday, September 22nd.

We had a wonderful, focused and funny meeting on Wednesday. About fifteen people came, and our youngest mathematician Avery B. at three was a trooper, playing rhythm games and lending us her arm to show the smallest cubit in the room - from a math joke her brother Will brought, about ancient Egyptians arguing about the length measures based on body measures. Wednesday, September 10th of 2008 was a big day in the history of the humankind, and not just because the Wednesday math clubs started The Large Hadron Collider, a particle accelerator designed for basic physics research, has started its operations, too. It is huge, expensive and exciting, and it is on all the news, and we talked about it a little bit in the club. I'd like to offer you a short funny rap video about it.

We started from introducing ourselves and sharing math jokes. Why are there so many jokes about number 8? "Why is six afraid of eight? Because 7, 8, 9! (seven ate nine)." Or this: "What is the half of 8? It depends on which half you take - the top half is 0 and the right half is 3!" Or this: "What did 0 say to 8? 'Nice belt!'" Here is your first quest: put the jokes you brought yesterday into the Natural Math joke collection, called LOLmath.

Our first big activity, called Zany Stars, was about our names. We always start club meetings from an activity about names. We took letters of our names, made up words starting with the letters, and then tried to figure out all pairwise combinations of words. How many are there? The easiest way to see them all is geometric! You make a polygon with as many corners as there are letters, and then connect them all. People selected words that were meaningful and fun for them. Finding out what each combination meant created new meanings, sometimes profound, sometimes whimsical. Combining individually meaningful pieces randomly is a very powerful way to brainstorm, used in many cultures, systems and pastimes, from casting Tarot cards to grabbing two random Shakespeare sonnets to jump-start a developers' meeting. Here are a few examples from club members' creations:

HANNAH H=happy N=need HN=gladness

WILL W=water I=ice cream WI=melted ice cream!

KARAN A=amazing N=new A=acknowledging AN=new apples NA=learning

EMILY E=elephant M=monkey EM=jungle

MATTHEW W=work T=today H=helping E=everyone WT=money HE=good reputation

AVERY A=apple E=earth R=read AE=orchard AR=Johnny Appleseed story

Here is your second quest: upload your beautiful math stars to a temporary gallery for the club. Simply attach your picture or story to a reply to this topic. You can color your name star and make it not only meaningful, but also beautiful. If you don't have a scanner, bring your star to the next Club and I will scan it for you. The programmers of Phenix Solutions, the company making software for Natural Math, will create a "star maker" and a permanent gallery for Zany Stars.

After the name activity, we went outside and played a ball rhythm game about names, followed by Human Knots. In the Human Knot game, we grab each other's hands randomly and then untangle the resulting mess. We started with all left hands and then grabbed all right hands. Both times we tried, the knot was of O1 type, equivalent to a simple loop (or letter O). I wonder if we need to grab left and right hands at the same time to make something like a trefoil knot or other more complex knots. You can find a mathematical knot classification and many stories about them here - just click on each knot to go to its page!

The knot game and a snack break was followed by another word activity: My Sequence Poem. Each particular type of a poem is characterized by its meter - the regular pattern of the sounds the verse makes. For the Sequence Poems, we created our own sequences and then based poem meters on the sequences, placing as many syllables in each line as the sequence told us. Counting syllables is one mathematical feature of poetry meters among many, and it was a good start. What to do if you get stuck creating a poem? Look at what other club members do for inspiration. Think of what you did today and make a poem about that. Or grab an interesting object and describe it! We used a kitten for the purpose. Cats are so metaphorical! To quote "Cats" the musical: "The mystical divinity of unashamed felinity." The activity was suggested by Elizabeth R., who sent us links of the Fibonacci poetry from the New York Times site. Here are a few sequence-based poems from the club members - some fancy sequence work here!

0,3,2,5,4,7
The jumper sequence, by Hannah
In the sun
Much fun
Says the mouse and cat
You don't see me
I'm way over here says the mouse
How do you know because you're the cat
Not so fun in the happy sun

1, 2, 4, 5 square and add one
The felinical sequence, by Courtney
Tense
Cat leaps
A mouse gasps
Jaws snap like his back

3,6,9,12
Emily sequence
The rabbit
Ate carrot and lettuce
And slept in the sun, the birds flew by
The rabbit was silent for he did not want boots awake

1,2,2,3,3,3,4,4,4,4
Repeat, repeat, repeat! By Shalu
Gold
real rich
solid blocks
gold medal
Olympics
jewelry
beautiful gold
everywhere
luxurious
precious metal

Probably the oldest and the largest web site about sequences is here. You can enter the start of your sequence and see if other mathematicians have discovered it already, and if so, what it is called and what interesting properties it has. For example, I learned that Shalu's "Repeat, repeat, repeat!" sequence appears in no less than nine different math books, and Courtney's Felinical sequence has to do with whole-number solutions to n = x^2 + y^2, an important math topic. Here is the next quest: type your sequence poem, explain how to make your sequence, and submit to the club's gallery.

I have another minor organizational quest: ask kids who have emails to email me, so that I can make a list. It will help them communicate to each other. I keep the lists very private: only club members will ever see them. And here is a big important quest: think of what we can do together to make beautiful, fun, meaningful, useful math. Anything you like to do, from soccer to home improvement, from animal care to cooking, can be a basis of an activity. Bring some ideas for the clubs.

I am looking forward to seeing you in two weeks on Wednesday, September 24th, at 9:30 am, and seeing your work in Natural Math galleries. Have fun and productive two weeks!

About twenty people met last week for the first Friday club. After a brief introduction and a discussion of our interests, we started the first activity, Zany Stars. We took letters of our name and made each one into a corner of a polygon. Then we connected each pair of letters we could possibly form. Each letter stood for something funky and meaningful, and then each PAIR stood for the connection between the letter notions. Here are a few examples from Friday. The connections are sometimes startlingly unexpected, sometimes directly logical, and sometimes funny and enigmatic:

ZAK
Z=zoom
A=act
ZA=improv

CAROL
C=children
R=reading
CR=Winnie the Pooh

JEAN
J=jump
A=action
E=earth
JE=earthquake
JA=bunjee jumping

CARLY
C=cat
Y=yellow
CY=tabby

SASHA
S=science
H=Haloween
SH=evil chemist

CONOR
N=nuclear
C=Conor
NC=Conor made of nuclear waste

JOSH
J=jungle
H=happy
JH=Jungle Book

GABE
A=ant
G=goo
GA=antestines

CHLOE
O=orange
E=enormous
OE=moon

SYDNEY
Y=youth
S=science
YS=explosion

ETHAN
T=teeth
H=help
TH=toothbrush

I am starting to write a description of the software that would support this activity. At first, I thought that "stars" would be the shapes made by connecting letters. However, depending on how many letters you have in your name, the resulting figure can be very far from a star. So I am thinking to make it so each letter is a star, and what people form out of them are constellations. By the next club, I should have some software sketches that we can look at together. I want to pick your brains on how to go about making it!

After the name connections, we played outside making Human Knots. If you start with all right hands grabbing each other and then all left hands, the resulting knots are of O-types, though there can be several of them. In our case, on the first game, the sisters Carly and Chloe took each other's right and then left hands and formed their own separate O-type knot as the result, of course! Theoretically, you can clasp your own hands together for a short human knot, but that seemed a bit silly! However, if you grab hands indiscriminately, left and right hands at the same time, the resulting knots don't "untangle" into O-shapes, because they are of different types. I think at some point we made a knot equivalent to the trefoil, but it was hard to say for sure. Here is a site we used to look at knot types. You can click on each knot for more pictures and stories about it. Some knots, like the trefoil I mentioned, have rich and twisted (I know, I am bad with puns) histories.

We had a snack break after the knot game, and watched a trailer of "Flatland: The Movie." The DVD I ordered just arrived, so we are going to watch it next time. It is about half an hour long: a dramatic, metaphoric adventure of a character breaking free of the restrictions of his two dimensions. It is based on a well-loved book by the same name, so old it's already copyright-free. Here is the full text online, with volunteers already recording it for free audio as well, but if you like paper books, here is an annotated edition at Amazon.

While we are on the subject of breaks, I want to take a break from math stories and talk about a meta-topic. Sometimes club members disengage from activities, which is of course to be expected during a meeting two and a half hours long. However, my ideal is for everybody to actively participate most of the time. I am still trying to figure out how to do it in smooth and cool ways, but if I see somebody taking a long break, spacing out for longish times, or walking away from the center of activity when people are aggregating, I will probably call them back in some manner. I am going to quote my daughter Katherine on it. On Monday, she sat in a corner playing with a construction set while everybody else sat in a circle taking turns talking about a definition we were making, and I called her into the circle and insisted she actually came. Afterward, I asked her if it was a good thing to do, at the end, and she said: "Yes, it helped, because if I am outside like that, it's bad Feng Shui, bad energy." Well, it's not literal, but "energy" is a good metaphor here: a person doing something alternative in the same space can be a strong distraction for everybody, ebbing the flow of an activity. I guess my rule of thumb will be - if you normally participate in the club actively, I will try to keep you inside activities. If you normally participate peripherally, like some three and four year old siblings, I will try to help you be content and non-distracting to others. If you have to suddenly disengage, say, if you get a phone call you have to take, or get inspired to write down a brilliant formula and need to get away from what others are doing, it may be prudent to take that call or break in another room or outside. I work very hard on designing and finding engaging and meaningful things to do, and so do all club members who suggest activities. But of course accidents happen; if an activity happens to bomb and is boring and not engaging, we can all work on fixing it or finding a better one together. What do you think?

After a break, we created sequences and based poems on sequences, counting out syllables. I am constantly at the variety and inventiveness of sequences people create during this activity. Just look at some of them!

1,2,3,4,5,6,7,8,9,10 =>1,3,7,15,31 (mark out as many as the previous number)
The Zak sequence
Me
I am cool
I do lots of cool stuff
Lots of stuff I do is cool you see my dear Josh the dude

6,8,7
"I don't know" sequence, by Sydney
Summer fun at the beach
Pink seashells and pearls in clams
Swimming and surfing such fun

7,6,8,7,5,9,7,4,10,7,3,11,7,2,12,7
Sugg sequence

Boy, I watched too many bubbles
7 movies this month but the
weather causes to syrup toes A the atomic

Elizabeth R. suggested the activity, sending me this link about Fibonacci poetry. Try to find if other people have already discovered your sequence, and if so, what they did with it, at this sequence research site. For example, Sydney's creation, the rule for which she jokingly named "I don't know", is a part of 735 different sequences, some of them with pretty cool names, like "Number of simple gatomorphisms of type B." Maybe we can submit club creations to the site, as well?

Oh, and people brought marvelous jokes! Even a poem, about happily exchanging a dollar for two shiny quarters, because two is more than one, and then quarters for three dimes, because three is more than two.

We could only type up a few examples. I would like to see the jokes you brought and all of your own creations at the Natural Math site. It will really help people who run similar clubs in other places, plus you can send the link to grandparents or friends to share what you did. You can type things up, or scan your work and attach a file. Simply reply to this forum thread.