kitchen table math, the sequel: a hamburger fold and a hot dog fold

Tuesday, March 11, 2008

a hamburger fold and a hot dog fold


hamburger fold




hot dog fold


Extra credit if you can guess me what a taco fold is.
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13 comments:

VickyS said...

I showed my 6th grader this post and said, "Can you believe this?" He responded, "I know those! We do it in school all the time!" "What classes???" "Math, science, language arts, everything."

Mmmm. Delicious!

March 11, 2008 at 9:01 PM
le radical galoisien said...

It makes me think of eigenvectors. Maybe it's because I have a linear algebra exam today!

March 12, 2008 at 4:27 AM
Unknown said...

A taco fold connects opposite corners, duh. What kind of 3rd grade teacher would I be if I didn't know that one!

March 12, 2008 at 7:35 PM
SteveH said...

My son loves Origami. They already have lots of names for different kinds of folds. Schools could even use folding paper for math. Oh boy! I'm thinking major educational product potential here. This is as important as fractals and tangrams!

Google Huzita-Hatori axioms

"The first 6 axioms are known as Huzita's axioms. Axiom 7 was discovered by Koshiro Hatori. The axioms are as follows:

Given two points p1 and p2, there is a unique fold that passes through both of them.

Given two points p1 and p2, there is a unique fold that places p1 onto p2.

Given two lines l1 and l2, there is a fold that places l1 onto l2.

Given a point p1 and a line l1, there is a unique fold perpendicular to l1 that passes through point p1.

Given two points p1 and p2 and a line l1, there is a fold that places p1 onto l1 and passes through p2.

Given two points p1 and p2 and two lines l1 and l2, there is a fold that places p1 onto l1 and p2 onto l2.

Given one point p and two lines l1 and l2, there is a fold that places p onto l1 and is perpendicular to l2."

March 12, 2008 at 7:58 PM
le radical galoisien said...

Is it really an axiom if you "discover" one?

Or was it a critical component to the space which they had missed?

March 12, 2008 at 8:30 PM
Independent George said...

Steveh - I think you could actually build a good exercise around those axioms - have the students try and prove each axiom using geometry & algebra, then derive general equations for the line of each fold.

Obviously, that's an enrichment activity outside the regular curriculum, but I can see the value to that. You can walk the students through the first proof, and each subsequent one should follow logically it.

March 12, 2008 at 9:14 PM
SteveH said...

"Or was it a critical component to the space which they had missed?"

I think it's just a translation of other axioms (proofs?) (Sorry, I'm an applied guy.) to paper. I have books that talk about things like constructing a line through a point and perpendicular to another line.

March 13, 2008 at 5:42 AM
SteveH said...

"... but I can see the value to that."

I was being cynical. I expect that most teachers would see that formality and run the other way.

My specialty is geometric modeling and I would like to see math classes deal more with basics like explicit, implicit, and parametric forms of equations, vectors, and matrix transformations. The math is not difficult, but the applications are immense.

March 13, 2008 at 6:07 AM
Independent George said...

I was being cynical. I expect that most teachers would see that formality and run the other way...

And I was being unrealistic. I think that's one of the appeals to fuzzy math; a lot of the activities actually could have instructional value, if combined with good, formal instruction. The problem is it's labor intensive, and highly dependant on the skill of the teacher, so that formal instruction usually never materializes. Instead, you get the paper folding, with none of the actual math that comes with it.

What's really funny/ironic/tragic is that those proofs & applications are exactly the kind 'higher-order thinking' skills the fuzzyists are supposedly focusing on (and, I suspect, what most parents assume is being taught). It's essentially a bait & switch scam; when someone says 'higher-order thining', the math-minded immediately think, "proofs". What we get paper-folding.

March 13, 2008 at 7:31 AM
LSquared32 said...

"Is it really an axiom if you "discover" one?"

It's a property when you discover it. If it's a property you want your space to have (if, for example, you want your theoretical space to have all of the same properties as paper), it is consistent with all of the other axioms you already have and you declare it rather than proving it. If it can't be proven using the previous axioms, then it is probably also a useful and worthwile axiom (rather than an axiom of lazyness).

A great many axioms get discovered or formulated as time goes by. I'm rather fond of Hilbert's axioms, for instance. I also try hard to convince my college students that SAS is an axiom, and not a theorem (my own personal pet peeve--I am not satisfied with Euclid when I could have Hilbert instead/as well).

March 13, 2008 at 2:53 PM
LSquared32 said...

oops, I left out a few words:

If it's a property you want your space to have (...), and it is consistent with all of the other axioms you already have and you declare it rather than proving it, then it is an axiom.

March 13, 2008 at 2:55 PM
LSquared32 said...

And my apologies to Le radical Galoisien. I expect he knows all this as well as I, it is merely one of the topics which have me on reflexive lecture mode.

March 13, 2008 at 2:57 PM
Catherine Johnson said...

I'm probably going to order an origami book any minute now.

Just as soon as I finish doing another National Geographic jigsaw puzzle.

WHICH ONE OF YOU TOLD ME ABOUT THOSE????

March 14, 2008 at 6:17 AM

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