Kotys Dad.................

[maverick2112]

Tessellations??????

1. What is a tessellation?
The filling of a plane or space with repetitions of a figure (or figures) in such a way that none overlap and there are no gaps.

2. What kinds of tessellations are there? Triangles or squares


3. How can you tell whether or not a polygon will "tessellate"?
vertexs must look the same and all angles must = 360 degrees


4. What are some ways to " make" tessellations?


5. What mathematical concepts can be taught using tessellations?


6. What "standards" can be taught using tessellations?

As you can see I am lost on this topic..........any help would be appreciated.

 

[Eddie Haskell]

Here you guys go again. Will you guys stop with this stuff. Showing off and all. But, let me try. Tessallation? Hmmmmm. Let me see..................

Tessellation? I got it. Tessellation is a word used in a song by U2. The song was entitled "Bad" and the live version was one of the best songs ever. Goes something like this.... a one and a two and a three............

.... isolation,

tessellation...........

let it go...........uh huh............. and fade away..............

Now, lets all sing the Name Game. Lets do Chuck.

Eddie

 

[maverick2112]

Showing off and all. But, let me try. Tessallation? Hmmmmm. Let me see..................

Not me Eddie...........You really probably know more of this stuff than myself................now Kotys Dad............thats another story..........it would takes me 100 sites on the web to research..........instead I just ask him first..............in his head is the madjacks residential" search engine" for anything mathematically related............now if we could figure out some mathetically related formula for who is going to cover tonight......he could probably figure that out also

 

[Eddie Haskell]

Mav:

I know from another thread that this guy is this websites genius. My vote for MVP (most valuable poster) in the Math catagory has to got to Kotyspop. In the computer catagory, my vote goes to KMA. As far as the animation catagory, my vote goes to my dear friend in Bowling Green, Kentucky, Dogs that Bark aka Wayne. All of his posts come from the land of make believe.

Eddie

 

[KotysDad]

Re: Kotys Dad.................

Mav,

The first 3 are easy to answer, the rest I have to give some thought to.

A tessellation is just what you said. Think of a soccer ball and how all the 6-sided figures (hexagons) fit together without overlapping. Thats a tessellation. You can only do it with 3 figures: triangles, squares and hexagons. The answer to number 3 is these are the only 3 figures you can tessellate because the requirement for a regular polygon to tessellate is that its interior angles be a divisor of 360. Triangles =60 Squares = 90 and Hexagons = 120. The next divisor of 360 is 180, and 180 degrees is a straight line, so it would be impossible to have a closed polygon from a straight line.

Your last 3 questions are a bit tougher. Let me think about them some. Email me at my hotmail account (Jack, I dont have a problem with you giving it to Maverick). My response might be a bit lenghty, so no need to bore (read: show off) the other readers.

 

[TORONTO-VIGILANTE]

always wanting to eeeejumacate myself so one day i'll be able to even TIE one of KotysDad's shoes....

1. What is a tessellation?

simple explanation for those that care:

here

 

[TORONTO-VIGILANTE]

furthermore, without tessellation we would not be able to enjoy our fine patterns in tiles, mosaics, quilts and art. :shrug:

(did a math lesson plan on it in teacher's college....) lol!!!

riffed from here: look

and another one:

 

[KotysDad]

TV,

I thought about that quilt thing too, and used to remember the quilts my grandmother used to knit when I was a kid and how they had these patterns in it. Of course, as a 6 year old at the time, I didnt know the work tressellation. lol

Mav,

Back to the other questions, without being too wordy cuz I couldnt come up with too much information.

Making them just requires using triangles, squares and hexagons in a series of patterns. There are certain rules (as one of those sites TV pointed out). Making them isnt as easy as just stringing along those polygons in any random fashion. There are sites that show how to do this, but its way to hard to explain in text. You have to constuct your patters so that all patterns have the same "center" (vertex) no matter how you rotate it.

That rotation goes back to the last post you had, about rotations and reflections. One is a good lead in to another.

As far as mathematical concepts, one thing about these patterns stick in my head......spatial reasoning....something I absolutely SUCK AT. When I open up these puzzle books, and I see a puzzle with these tressellations and they ask, "How many squares do you see" or "how many triangles are there in the picture".....they drive me crazy. My brain isnt good at spatial reasoning problems. Engineers and mechanical designers are good at this kind of stuff. But, it is a good way to teach this to students - to introduce them to tressellations.

I have no idea what your teacher means by "standards" to answer the last question. Sorry.

 

[maverick2112]

Thanks again.........maybe I can get your email from MJ and send you a gift or something for all the help..........it is sure appreciated.

 

[KotysDad]

Mav,

You're welcome. No need for compensation. I do it purely for the enjoyment of helping out and loosening some old cob webs from the past.

If you're ever in my part of America, or vice versa, you can buy a round of drinks.

:toast: