Mathspig has gone all wallpappery this week. We are going to have some fun with symmetry, patterns, 3D mirror images and 3D rotations. So get ready mathspigs and GO, Go, Go
Now, my Sweeties, I want you to understand something important about the way people, who use maths, think.
It is vital that architects can walk around inside an imaginary building in their heads, that engineers can see in their imagination where the support columns need to be placed in a building/bridge, that chemists can visualise 3D mirror images of molecules, that fashion designers can see the axis of symmetry and also invert an item of clothing inside out (because that is how clothes are sewn), that designers can rotate objects in their imagination (not just to look pretty, but to make sure the object can stand up) and it is important that computer programmers can see patterns to write their repeating algorithms (More later).
The maths involved here includes:
Symmetry
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2D patterns
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2D & 3D mirror images
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3D Rotations
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Algorithms
You will find these fab world maps @ BLDG BLOG, which uses an algorithm to map the 3D world into different 2D shapes, which can then be reconstructed into 3D objects. Wow!
Sometimes mathspiggies, teachers forget how important these visualising exercises can be in the development of maths thinking skills.
So my little Sweeties, we’re going to use some of these maths skills to build up your maths brain.
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1. Rotating Tessellation
A tessellation is a repeating pattern with no gaps like floor tiles.
Look at the pattern. It involves equilateral triangles repeated.
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Oops! Not exactly perfect, but Mathspig was using paper and scissors!
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We aren’t going to write a computer program, but rather think what we might want the program to do. The Rotation Tessellation algorithm would go something like this. Take triangle shape, rotate around fixed point A until area tiled, stop. Take new fixed point, rotate new shape around this point until all area tiled, repeat, repeat, repeat.
2. Flip Tessellations
This time we will use mirror images, which we create by flipping an image.
As the Eurovision Song contest has just finsihed we’ll use an image of the Twin Brothers Jedward to create our flip tessellation. You can use any image to create a flip tessellation, even your own head!!!!!!!!! First I took one brother.
Then I flipped him horizontally.
Then I flipped him vertically
and then I just kept going.. unfortunately, I had to print and scan to get the wallpaper effect.
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We could create an algorithm, which tells the computer to do this: Take Jedward 1, flip horizontal, flip last pic vertical, flip last pic horizontal, copy new pic, flip horizontal, flip vertical, flip horizontal, repeat, repeat…………….
In fact, Mathspig had an JEDWARD algorithm in her head, copy, paste, copy, paste, copy, paste….. Arghhhhhhh! ….couldn’t stop…..
But you end up with a lovely set of JEDWARD floor tiles, or curtain fabric or maybe shirt material!!!!!! Nice! It depends on your taste, really.
As part of our Mid-year/ End of year madness here are some crazy things to do with Lego.
The idea with these projects is to challenge you, my pretties, by giving you the Lego, the time and the inspiration so you can go, go, go for it and, maybe even, surprise yourself.
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1. Going Loopy
Can you make something round from oblong Lego blocks?
Lego constructions can move. Here is The Blossoming Lotus built by the Brickengineer. If you click on this link you can see the Lotus blossom. Cool! Can you make a Lego flower bloom, mathspigs?
But if you really want to see some Lego flowers bloomin’ get yourself down to the Reiman Gardens @ Iowa State University. They have the Lego flowers, the Lego birds, the Lego butterflies, a Lego Zoo. Perhaps, mathspigs, your class could put your heads together and make a Lego garden or a Lego Zoo.
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3. Going Square
Lego artist Nathan Sawaya’s Lego sculptures are mind boggling. You can find the following sculptures @ sayhi-todesign blog spottoor @ Nathan’s own blog, The Art of the Brick. Maybe, mathspigs, you could build a geometric sculpture out of Lego blocks.
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Or get inspired by Nathan Sawaya’s other sculptures
Wow! That’s just how Mathspig feels when I’m waking up in the morning.
Another way to get your brain wrapped around the idea of symmetry, 2D patterns and 3D image rotations is by building a musical instrument and some of them even play music, um, sort of!
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1. Lego Harpsichord built by a kid
with ordinary Lego that works!!!
2. Lego Electric Guitar that really works
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3. Lego Flute that works
They say it works. Mathspig hasn’t heard it. The kid could be just spending time blowing on a Lego block.
Here is another art work by Lego artist Nathan Sawaya. The cello doesn’t play music, but this is such an awesome video of Nathan building the cello, it is a MUST see, mathspigs.
It doesn’t play music, but think about it mathspigs. It would look soooooo cool sitting in your bedroom. Besides, many a guitar sits in a bedroom without being played.
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6. Lego Saxaphone
Here is another work by Pat Dube. It doesn’t play music but it’s just cool, man. Put on those sunglasses, feel the vibe and chill.
Now mathspigs, let’s get mobile. There is a lot of symmetry and 3D rotations involved in building a Lego ca. You can go low -tech or high tech. Get ready mathspigs here we go:
1. Lego Balloon Car
I don’t think you’ll need instructions for this one. Maybe you could pimp that ride, mathspigs.
Mathspig toddled along to the Melbourne Comedy Festival to see Stand Up Mathematician, Matt Parker, and BBC wit, Timandra Harkness, in Your Days Are Numbered: The Maths of Death.
It was Ha! Ha! or, as we mathspigs say, (Ha)2 Hilarious.
Almost Therapy.
This is the break through geeks of the world have been waiting for. Not just jokes about mathematicians, but jokes involving MATHS!!!!!! Here is a MATHS OF DEATH statistic for the no. of Americans killed by cows each year. You might call this the Revenge of the Rump Steak.
Matt Parker is based in the maths department at Queen Mary, University of London and, as Matt says, he is now a fixture on the illustrious Mathematics speaking circuit. He writes maths columns for The Guardian, UK. More @ Stand-upMaths. Matt is from Perth, Australia.
Timanadra Harkness spent 5 years in standup, co-wrote a film, No Future in Eternity, about a man going to Mars in his hall cupboard and appears on the BBC panel show, Mind Games. Otherwise she fills in time writing articles for Wired and The Daily Telegraph. More @ Timandraharkness
Here is an absolutely true to form hilarious skit of Matt in action not so much doing maths as very much acting like a maths teacher when his iPhone is stolen.
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Inspired by Matt and in the not very long tradition of standup maths mathspig has added some funny activities in the following posts.
Here is standupmaths comic Matt Parker doing calculations in his head including a bar code calculation.
Thanks to Matt making the barcode calculations look EASY Mathspig spent about 12 hours blowing steam out her ears and tearing up packaging trying to get the barcode maths to work.
This is THE absolute best exercise to test accuracy in simple calculations including transcribing numbers, which are so easily misread. It also shows you how BARCODES work.
The cash register pings if the BARCODE CHECK DIGIT Algorithm matches the CHECK DIGIT, which is the last digit in the barcode. This is how the cash register computer checks that the data in the barcode has been transferred correctly. All data transfers have some sort of data check algorithm.
The PING is KING!!!!!!!!
Mathspigs, you can check your maths skills by picking up the nearest product with a 13-digit barcode and calculating the CHECK DIGIT. The answer is at the end of the barcode.
Scientists, bless their little cotton sox, are always trying to calculate the funniness of a joke.
Jokes depend on the person, their mood and a zillion other factors. We’d say there are TOO MANY VARIABLES in maths. For instance, context rules. Titanic jokes don’t go down well on a sinking ship.
Note: y = 0 for no reaction and therefore funniness index is zero.
y < 0 for a frown make the funniness index negative.
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GOOGLE FUNNINESS ALGORITHM
Google created a funniness algorithm to rank funny videos in the You Tube Comedy Slam. The algorithm scores for views, comments (Funny, hilarious etc), laughter sounds (hahaha), web acronyms ( lol, lmao, rofl), (c) funny, emoticons , and repeats (lololololol, loooooooool )
And the winner is: NO NO NO CAT
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FUNNINESS MATHS EXERCISE
or the DAD-Joke-O-Meter
Dads, Uncles and Some Teachers tell really dumb jokes. Dumb jokes are called Dad Jokes.
So you wanna be FAMOUS and fabulous and uber-cool too.
Maybe you wanna be the Chris Rock of maths. Being famous is soooooo cool.
…………….……You get attitude!!!
……………………You Get cool sunglasses!!!
….You get a chauffeur that’s not your mum!
But what are the chances? What is the probability that a kid at your school will become famous one day? Cate Blanchet went to Mathpigs kids’ school. But in Australia we don’t make a fuss. They haven’t put a picture of her on the wall or anything.
So mathspigs let’s work out the probability of you becoming a STAR, BABY!
The first question is how do you measure fame? Do you have to be on TV to be famous? Do you have to be a Hollywood star? Should you be a wax dummy in Madame Tussaud’s? Not as a job. I mean because you are so fabulously famous.
Perhaps, you could use Tom Weller’s humorous Rictus scale (a parody of the Richter Scale) for earthquake intensity using media coverage as a guide to fame. Just replace the persons name for the word ‘scene’.
I’m thinking around ’5′ looks like FAME, but you decide. Now count how many ex-students from your school (and any current ones) who have become famous in the last 20 years and do the maths.
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Rictus
Scale #
Richter Scale
Equivalent
Media Coverage
1
0-3
Small articles in local papers
2
3-5
Lead story on local news; mentioned on network news
3
5-6.5
Lead story on network news; photos in nation newspapers; governor visits scene
4
6.5-7.5
Network correspondents sent to scene; president/PM visits area; commemorative T-shirts appear
5
7.5 up
Covers of weekly news magazines; network specials; “instant books” appear