Lego Mania 1: Going Loopy

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?

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You will find more awesome Lego Loops at Discovery News and more cool curves and loops @ Sanders Brick Bending Blog

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2. Going Bloomin’ Crazy

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 spotto or @ 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.

Lego Mania 2: Going Musical

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.

More @ Izakoo Blog Spot

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4. Lego Cello

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.

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5. Lego Guitar

This one is by Patrick Dube

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.

Lego Mania 3: Going, Going, Gone!

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.

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2. Lego Rubber Band Car

You will find instructions @ eHow     

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3. Cool Lego VW

Ramping up the challenge, how about building a Lego street car.

If you have a Lego Car Kit you can make a really cool VW and a cool video clip as well:

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4. Lego Street View Car 

If you are the ultimate geek then this is the Lego car project for you. It could take years, mathspigs, but worth the sweat.

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5. Lego Bike

Or just get on your Lego bike.

Sean Kenney is a Lego Artist. You can find more images @ incredible things and more amazing Lego art works @ Sean Kenney’s own website.

More amaaaaazing machines @ Lego Education UK

 

Get Ready for the Lego Olympics

Get ready mathspigs. You need one Lego Man, Girl, Vampire or Alien each for this exercise. Now we are going to set out the Lego Olympics Athletics track.

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But this story of the Olympics begins with Carl Lewis, one of the greatest athletes of all time who won 9 Olympic Gold medals in 100m, 200m, relay and long jump.

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Carl Lewis

Mathspig needs to find out how big the Lego Olympics track would be. How? Easy.

Carl Lewis will be our standard Lego Man.

I chose Carl Lewis because he kindly gave me his autograph once when I sprinted in high heels across a ballroom floor at a sports dinner in Melbourne and beat all other journalists.  It was my personal best in high heels, I think.

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This means everything at the Lego Olympics  will be

1:50

of the real Olympics.

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The  Lego Bird’s Nest Stadium @ Beijing will be 1/50th of the real Bird’s Nest Stadium. (Not the scale shown here). Pictures by Johor Bahru.

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The Lego Beijing Water Cube Swim Centre will be 1/50th of the Real Water Cube.

EXERCISE 1:

Now mathspiggies over to you. The first thing to do is calculate the Lego Olympic measurements (table below). 

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EXERCISE 2:

Then mark out a Lego Olympics 100m sprint to scale and/or

draw a Lego Olympic track (in chalk, perhaps) and/or

step out a Lego Olympic marathon track and/or

make a pole vault pole to scale for your little Lego Man.

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Structure	Real Olympics	Lego Olympics
100m Sprint	100m	2m
400m Sprint	400m
42 km marathon	42,000m
Olympic Pool Length	50m
Olympic Pool Width	25m
Olympic Rowing Course	2,000m
Equestrian Jump Height	2m
Approx Pole Vault Pole Length	5.5m
Javelin Length Men Women	2.6m 2.2m
Olympic Stadium Straight Segment Semi-circle Radius inner Lane Lane Width	84.39m 36.50m 2.5m

Lego Olympics Flags

The Lego Marching band is rehearsing for the Opening ceremony.

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Here are just a few of the weird and wonderful folk from the many planets and nations represented at the Lego Olympics:

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………….Bandito (Republic of Baddies)

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Mr Boopy (Bozonia)

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Gorilla Suit Guy (Halloweenotopia)

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………………..Barry the Butcher (Alien Steakistan)

……………..BioHaz (Toxorama)

…………………Dead-Eye Doc (AyeAwArghia)

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Dr Jabb (Bummerville)

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Hula Lula (Grinmania) 

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1. Flag Fractions

EQUIPMENT: Mixed Lego Blocks

Here is the maths. It’s fractions. It’s simple.

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A. National Flag of  Comotosia

They’re a bit sleepy in Comotosia so you better design a flag to wake them up, mathspigs.

The flag must measure ………….   6 blocks x  12 blocks.

One block is a 4 bumps blocks (See pic). An 8 bumps block equals 2 blocks.

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Here’s the catch, mathpiggies.  1/4 of the blocks in the flag must be RED.

How will you do this? (Hint below)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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.B. National Flag of Bordom

Once again the Bordonians need a lively flag.

The flag must measure 6 blocks by 12 blocks, but this time it must contain 1/4 red and 1/3 blue. How do you do this?

Hint: Mathspigs! You will have to count the number of red and blue blocks.

 

2. Design A National Flag to Lego Scale

First, name your Lego man, girl or alien and pick a name for their country, planet or crypt.

You will be drawing two flags.

All national flags are rectangles except Switzerland and Tibet, which have square flags but not at the Olympic Games.

Olympic Flags measure:  150 cm x 90 cm

or …………………………….. 60 inches x 35 inches.

These sizes are not equal so which flag is bigger the decimal flag or the Imperial Units flag?

The Imperial units flag is 152.9 cm x 88.9 cm. It turns out the area of the Decimal flag is 13,500 cm² and the Imperial Flag 13,593 cm² . 

You will be designing a decimal flag.

Note the Flag ratio of length: width = 150 : 90

…………………………………………………… =  15 : 9 = 5: 3

First design a flag with 5: 3 ratio.  One measuring 10cm x 6 cm would be ideal.

 

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How big are the national flags at the Lego Olympics:

Real flags at the Olympics =  150 x 90 cm

Lego Flag measurements =  150/50 x 90/50 = 3 cm x 1.8 cm = 30mm x 18 mm

Here are my two Lego people with flags  I prepared earlier:

The Enforcer from the Constellation of Obeymia and Mr Boopy from Bozonia.

Lego Olympic Opening Ceremony

The Lego Olympics must begin with a

triumphant Trumpet Fanfare.

Here is the US Army Herald Trumpets playing a rousing fanfare:

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Marching Maths

Three nations are marching one after the other:

Pajamaramas (PJ Boy flag bearer),

The Crytomanians (Mummy’s Boy flag bearer)

and the Berserkers (Olag the Viking flag bearer).

But there is a problem.

They march around the Olympic Track, which is a 400m circuit (inside track).

Lego Olympic Track Circuit = 400/50 = 8 m

But the Pajamaramas, the Cryptomanians and the Beseerkers all walk at different speed. They could just bump into one another and end up in a big heap. So how much time should the officials allow between each country so they don’t collide on the track.

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Speed S₁

PJ Boy is a really slow walker

Real life Really Slow walk = 3.0 kph = 3000 m/hr

……………………………………………….= 3000/60 = 50 m/min

Lego really slow walk=   50/50 = 1 m/min

Speed PJ Boy = S₁ = 1m/min

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Speed S ₂

Mummy’s Boy is a slow walker

Real Life Slow walk = 4.5 kph = 4500 m/hr

………………………………….  = 4500/60 = 75 m/min

Lego slow walk = 75/50 = 1.5 m/min

Speed Mummy’s Boy = S ₂  = 1.5 m/min

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Speed S₃ 

Olag is a fast walker

Real life fast walk = 6 kph = 6000 m/hr

……………………………… = 6000/60 = 100 m/min

Lego really slow walk = 100/50 = 2 m/min

Speed Olag = S₃  = 2m/min

 

Lego Track Circuit = 8m

Time on circuit (T) in mins:

T = d/S

T = 8.0 /S

The time each nation takes to finish marching around the track will be:

T₁ = 8.0/S₁  = 8.0/1  = 8 mins

T₂ = 8.0/S₂ = 8.0/1.5 = 5.3333 = 5 mins 20 secs

T₃ = 8.0/S₃ = 8.0/2.0 = 4 mins

If you started them all at once there’d be a real pile up.

 

March Time with 1 min gap between groups:

The Enforcer from the Constellation Obeymia will make sure each marching group leaves exactly on time. He will set the clock ticking at 0 mins then enforce a one minute gap between each group.

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Look at the times each nation finishes marching around the track now:

PJ Boy…………………………………………………………………………..

and the Pajamaramas ……………………………………………..8 mins,

Mummy’s Boy and the Crytomanians ………………. 6 mins 20 secs

and Olag and The Beserkers start 2 minutes after PJ Boy and Co and finish at …………………………………. 6 mins.

They will still collide on the track!!!!!

Here are the results for different gap times:

 

 

Nation	March Time Gap time 0 min	March Time Gap Time  1 min	March Time Gap Time  2 min	March Time Gap Time  3 min
PJ Boy + the Pajamaramas	8	8	8	8
Mummy’s Boy and the Crytomanians	5mins 20 secs	6 mins 20 secs	7mins 20 secs	8 mins 20 secs
Olag and The Beserkers	4	6	8	10

The 3 minute gap works!!!

I think we need a round of applause:

Why not ALGEBRA?

If you had to do this calculation for the entire 205 nations at the 2012 Olympic Games, you can see that your brain might explode.

Da-DA! We can use algebra.

Here is a formulae:

T = d/S + nt_g

where

T = time (mins)

from beginning of ceremony.

d= track circuit distance = 8 m

S = speed m/min

n = nation march order number = 0,1,2,3,etc

t_g = time gap between nations (mins) = 1, 2, 3, 4 etc    

TRY IT, mathspigs!!!!!

Lego Olympics Triathlon

This is the Lego Triathlon.

And, mathspiggies, your Lego Man/girl/alien has made it into the finals. 

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EQUIPMENT: Your Lego Man, girl, alien, your brain, a calculator & one dice.

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In the Olympic Triathlon contestants:

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Swim 1.5 km = 1,500 m

Cycle 40 km = 40,000 m

Run 10 km = 10, 000 m

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In a Lego Olympic Triathlon little Lego men, girls, aliens have to:

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Swim 1,500/50 = 30m

Cycle 40,000/50 = 800m

Run  10,000/50 = 200m

But each contestant will be better at some section than another.

Your Lego man, girl, alien replaces one of the following contestants. Transfer their number and times to your column.

Now calculate the Total Times for each contestant.

THEN roll the dice.

3. Disqualified because your coach gave you an alien Smoosnot drink with banned drugs by mistake.

5. Disqualified because a Groppanator from the Urgastor Galaxy ran out of the crowd just before the finish line and hugged you with his 6 arms.

Triathlete	30 m Swim Speed + Time	800m Cycle Speed + Time	200m run Speed + Time	Total Time mins	Roll 3 or 5 Disqualified
1 Mummy’s Boy from Crytomania	40 m/hr ……………	400 m/hr ……………	250m/hr ……………	………….	…………..
2 PJ Boy from Pajamarama	30 m/hr ……………	200 m/hr ……………	500 m/hr ……………	………….	…………..
3 Olag from Beserk	40 m/hr ……………	200 m/hr ……………	500 m/hr ……………	………….	…………..
4 Dead-Eye Doc from AyeAwArghia	60 m/hr ……………	400 m/hr ……………	450 m/hr ……………	…………..	…………..
5 Hula Lula from Grinmania	50 m/hr ……………	400 m/hr ……………	500 m/hr ……………	………….	…………..
6 Mr Boopy from Bozonia	30 m/hr ……………	600 m/hr ……………	200 m/hr ……………	…………..	…………..
7 Gorilla Suit Guy from Halloweenotopia	50 m/hr ……………	500 m/hr ……………	300 m/hr ……………	…………..	…………….
8 BioHaz from Toxorama	60 m/hr ……………	500 m/hr ……………	400 m/hr ……………	…………..	…………..
………………… from ………………..	…………… + ………………..	…………….. + ……………..	…………….. + ……………..	…………..	…………..

Who won?

You can work it out mathspigs.

Total Times are published @ the end of The Lego Olympics Closing Ceremony.

Lego Olympics Closing Ceremony

The closing ceremony is chaos. All the athletes crowd together.

There is one last lot of calculations, mathspigs.

Think about this.

% Gold Medal Winners:

At the 2012 London Olympics there will be 47 Gold medals awarded in athletics.

There will be 2,000 athletes competing for these medals. Now some athletes will win more than one Gold medal and some events eg. the relay race involve more than one athlete. Each member of the winning relay team wins a Gold Medal.

Approximately what % of athletes won’t win a Gold Medal at the London Olympics?

Ans:  97.65%

Probability of Winning a Gold Medal:

Ha-HA! Tricked ya! Such a calculation would be meaningless.

The core to all probability is, or should be, RANDOM SELECTION.

Lottery balls fall randomly into the tube. But the Olympic athletes represent a BIASED SAMPLE. Athletes are selected for the games. They must qualify for an event. They train. The chance of one athlete winning is quite different from that of another.

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Eight numbered  100m-sprint athletes is a Biased Sample.

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Eight numbered lottery balls in last nights draw make up a random sample.

This brings us to the end of the Lego Olympics.

We will finish with this end song by Lego Rock Band and some Lego fireworks.

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Lego Olympics Triathlon total Times: 1. Mummy’s Boy: 3 hrs 33 mins, 2. PJ Boy 5 hrs 24 mins, 3. Olag 2 hrs 51 mins, 4. Dead-Eye Doc 2hrs 57 mins, 5. Hula Lula 3 hrs, 6. Mr Boopy 3 hrs 20 min, 7. Gorilla Suit Guy 2hrs 52 mins,8. BioHaz  2 hrs 36 mins.