Archive for the ‘Olympic Maths’ Category
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June 27, 2016Get Ready for the Lego Olympics
February 23, 2012Get 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.
Or bring in a Lego Man/Girl/Pirate and step out the Marathon Track (840m to scale).
This little guy has to run 840 m!!!!! Wow!
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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 Semicircle Radius inner Lane Lane Width 
84.39m 36.50m 2.5m 
Lego Olympics Flags
February 23, 2012The Lego Marching band is rehearsing for the Opening ceremony.
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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)
…………………DeadEye 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.
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 cm^{2 }and the Imperial Flag 13,593 cm^{2} .
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
February 23, 2012The 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 S_{1}
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 = S_{1 }= 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 S_{3 }
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 = S_{3 }= 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:
T_{1} = 8.0/S_{1 } = 8.0/1 = 8 mins
T_{2} = 8.0/S_{2 }= 8.0/1.5 = 5.3333 = 5 mins 20 secs
T_{3} = 8.0/S_{3 }= 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.
DaDA! 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 Closing Ceremony
February 23, 2012The 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 were 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:
HaHA! 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 100msprint 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 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. DeadEye 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.
How fast are Our Olympic Athletes?
September 30, 2011First we have to calculate the speed or velocity of an athlete.
Event distances are recorded in m (The Olympic Games uses the Metric system) and time in minutes, seconds and 1/100ths of a second except cycling where 1/1000ths of a second are recorded.
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Here is Usain Bolt creating a New World Record for 100m in Berlin 2009. You may as well watch. It will take less than 10 secs.
We are going to use current Olympic Records to calculate the average speed of Usain Bolt, the fastest man on earth:
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But we are more familiar with km per hr (kph) so we will convert from m/sec to kph:
Some in the world use mile per hr (mph) so one more conversion:
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Maths Exercise:
Here are some current Olympic Records, which students can use to calculate average speeds in m/sec then convert these speeds to kph (See chart in the following post for answers);
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1. 100m M Sprint 9.69 sec Usain Bolt Jamaica
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2. 100m W Sprint 10.62 sec Florence GiffithJoyner USA
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3. 100m M Freestyle 47.05 sec Eamon Sullivan Australia
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4. 100m W Freestyle 53.12 sec Britta Steffen Germany
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5. 1500m M Freestyle 14.38.92 mins Grant Hackett Australia
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6. 200m M Butterfly 1.52.03 mins Michael Phelps USA
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7. 200m W Butterfly 2.04.18 mins Lui Zige China
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8. 1,500m M Track 3.32.07 mins Noah Ngeny Kenya
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9. 1,500m W Track 3.53.96 mins Paula Ivan Romania
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10. Marathon 42.195 km M 2.06.32 hrs Samuel Wanjiru Kenya
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11. Marathon 42.195 km W 2.23.14 hrs Naoko Takahashi Japan
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12. Cycling M 200m Sprint 9.815 secs Chris Hoy UK
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13. Cycling W 200m Sprint 10.963 secs Victoria Pendleton UK
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14. Rowing M 8+ 2000m 5.19.85 mins USA
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15. Rowing W 8+ 2000m 5.55.50 mins USA
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16. Cycling M 1km Time Trial 1.00.711 mins Chris Hoy UK
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17. Cycling W 500m Time Trail 33.952 secs Anna Meares Australia
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You will find more Olympic records at these links: track, cycling and swimming:
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How fast are Olymic athletes compared with animals?
The top speed of humans was clocked at 43.56 km/h (27.1 mph) by Olympic sprinters Michael Johnson and Donovan Bailey during their Olympic competitions. This top speed only lasts for very short bursts. More info at this link.
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I’m sure Usain Bolt would achieve an even higher burst of speed if being chased by a cheetah. And, of course, cyclists can go much, much faster down hill.
So lets see how our 15 athletes above would rank on the animal speed chart. Go to the next post. Woo HOo! It’s the Zebra Olympics.
Woo! Hoo! It’s the Animal Olympics
September 30, 2011Would a Cheetah beat an Olympic Cyclist?
Let’s find out …
The following table logs the fastest times recorded for various animals.
It’s like The Guinness Book of Records for Rats and other critters. Falcons do not fly at 350km/h at all times terrifying tourists. Nor does Usain Bolt race down the 3rd aisle at the supermarket in a few seconds.
This table compares the average speed of humans with the top speeds of animals. More info @ mistupid.
Animal 
MPH 
km/h 
Peregrine falcon 
217 
349.24 
Swift 
98 
157.72 
Cheetah 
70 
112.66 
Pronghorn antelope 
61 
98.17 
Wildebeest 
50 
80.47 
Lion 
50 
80.47

Thompson’s gazelle 
50 
80.47 
Quarterhorse 
47.5 
76.45 
12. Cycling M 200m Sprint Chris Hoy UK 73.43 km/h
Elk 
45 
72.42 
Cape hunting dog 
45 
72.42 
Coyote 
43 
69.2 
Gray fox 
42 
67.6 
13. Cycling W 200m Sprint V. Pendleton UK 65.67 km/h
Hyena 
40 
64.38 
Zebra 
40 
64.38 
Mongolian wild ass 
40 
64.38 
Greyhound 
39.35 
63.33 
16. Cycling M 1km Chris Hoy UK 59.30km/h
Whippet 
35.5 
57.13 
Rabbit (domestic) 
35 
56.33 
Mule deer 
35 
56.33 
Jackal 
35 
56.33 
17. Cycling W 500m Anna Meares Aust 53.02 km/h
Reindeer 
32 
51.5 
Giraffe 
32 
51.5 
Whitetailed deer 
30 
48.28 
Wart hog 
30 
48.2 
Grizzly bear 
30 
48.28 
Cat (domestic) 
30 
48.28 
Elephant 
25 
40.24 
1. 100m M Sprint Usain Bolt Jamaica 37.15 km/h
2. 100m W Sprint F. GiffithJoyner USA 33.91 km/h
Black mamba snake 
20 
32.19 
Race runner (lizard) 
18 
28.97 
8. 1,500m M Track Noah Ngeny Kenya 25.45 km/h
Wild turkey 
15 
24.14 
14. Rowing M 8+ 2000m USA 22.50 km/h
9. 1,500m W Track Paula Ivan Romania 22.21 km/h
15. Rowing W 8+ 2000m USA 20.27 km/h
10. Marathon M Samuel Wanjiru Kenya 20.02 km/h
Squirrel 
12 
19.31 
Pig (domestic) 
11 
17.7 
11. Marathon W Naoko Takahashi Japan 17.68 km/h
Chicken 
9 
14.48 
3. 100m M Freestyle Eamon Sullivan Australia 7.67 km/h
4. 100m W Freestyle Britta Steffen Germany 6.77 km/h
6. 200m M Butterfly Michael Phelps USA 6.44 km/h
5. 1500m M Freestyle Grant Hackett Aust 6.16 km/h
7. 200m W Butterfly Lui Zige China 5.80 km/h
Spider (Tegenaria atrica) 
1.17 
1.88 
Giant tortoise 
0.17 
0.27 
Threetoed sloth 
0.15 
0.24 
Garden snail 
0.03 
0.05 