Mathspig just loves this Fluid Geometry Mural by artist Clint Fulkerson. Here is a Speed Clip of Flulkerson at the University of Maine Art Gallery 2012.
Mathspig went crazy trying to produce her own Fluid Geometry Mural. These guys are artists. But your middle school maths class can use a simple method (See GIF below) and make a fab mural on a white/black board or down a school hallway. This is a great end of year/semester/pre-holidays project.
The reason for tackling such a project is to engage students, who are otherwise not interested in maths as well as do some whole school PR for maths. The mural WILL be noticed. And it makes maths look COOL.You will find more interesting Fluid Geometry works by Clint Fulkerson here.
The Pixar film, Finding Dory, began as storyboard sketches. There were 103,000 drawn for the film. The sketches are placed side-by-side in sequence in order to convey scenes and deliver a rough sense of how the story unfolds.
How many 64-page Exercise books would the story board take?
Only one side of the page of the 64-page exercise book would be used for storyboarding.
No. exercise books = 102,000/32=3,187.5
If put into flip Book form the story board sketches would produce a ‘rough’ version of the film.
Superman Vs Goku
………………………………………..
2. Ratio
If you are making a film about, say, Godzilla, you want him to be big. VERY BIG. But he has to share a screen with human characters.
If Godzilla is too big all the humans look like ants.
If he is too small … he looks like a toy TRex.
The Monster Maths:
Height: 108.2m Godzilla’s towering height in the 2014 film—the tallest onscreen incarnation ever
Tail: 167.74m Total length of Godzilla’s spiked tail
Volume: 89,724 m3 Godzilla’s total volume in the 2014 film.
Volume: 90,000 tons Godzilla’s volume if filled with water
Teeth: 1.07mLength from the root to the tips of Godzilla’s canine teeth
Teeth: 60 Teeth in Godzilla’s mouth
Roar: 4.83km Approximate distance Godzilla’s roar reverberates. (100,000W Power of the 3.7m-high, 5.5m-wide speaker array from which the sound designers blasted Godzilla’s roar to record the sound in a “real world” context)
Feet: 17.66mTotal width of Godzilla’s feet across the widest point
Feet: 18.18m Length of Godzilla’s footprint from toe to heel
You vs Godzilla
The average height for 14-year-old boys in the U.S. is 164 cm.
For 14-year-old girls in the U.S. the average height is 158.75 cm.
Godzilla = 108.2 m
We’ll assume an average height of, say, 1.6m for a 14 yo.
14 yo =1.6 m
Height:
108.2/1.6 = 67.6 = 68
Footprint
You vs Godzilla’s Footprint
18.18/160 =11.4
Teeth
You vs Godzilla’s Tooth
1.07/1.60 = 0.7
………………………………………………
3. 3D Modeling: Polygon Count
3D modeling can be approached in several ways. There is a good explanation here.
One method is to use a 3D scanner to produce a 3D mesh.
Godzilla model under construction
Digital Godzilla as 3D mesh
The mesh consists of polygons. You’ll find everything you want to know about polygons here.
The greater the no. of polygons the better the resolution in a 3D mesh, the better theresolution of the character or object as more shading and texture variation can be added.
So the POLYGON COUNT or POLY COUNT is a measure of the quality of an image.
Here are some POLY COUNTS:
Godzilla
500,000 polygons.
It took the 4 CGI artists 6 months to fully nail the texture of Godzilla’s scales. (See above)
Elysium
Just the space station ran close to 3 trillion polygons.
Transformers 2
Devastator had 13 million polygons
Clash of the Titans
The Kraken had 7 million Polygons.
Avatar
Apart from some bluescreen shots of live-action actors in cockpits, it’s all CG: gunships, missiles, smoke trails, water, fire, an army of photorealistic virtual characters and a giant tree made of 20 million polygons with 1.2 million leaves.
The POLY COUNT is always greater in animated movies than in video games mainly because a higher poly count takes longer and costs more. A higher resolution is needed in a movie as it is shown on a much bigger screen.
Gollum: Game vs Film 3D model
Here are some POLY COUNTS for some popular games:
The Amazing Spiderman
Spiderman – 11,652
Assassin’s Creed 3
Benjamin Franklin – 17,744
Charles Lee – 25,994
Connor Kenway – 28,501
Desmond – 14,934
Haytham Kenya – 19,985
Batman: Arkham City
Batman: Film Version
Batman: Game Model
Batman Beyond suit – 13,050
Harley Quinn – 17,731
Harley Quinn (DLC) – 19,110
Poison Ivy – 15,977
Call of Duty: Black Ops
Frank Woods (full gear) – 19,777
Crysis 2 (console)
Nano suit – 19,073
Multiplayer suit – 27,414
………………….
FREE 3D MODELING FOR MIDDLESCHOOL STUDENTS
TINKERCAD is the free online resource that allows students to create their own 3D graphs – like Godzilla vs You (above) or 3D images that can be used for 3D printing. Play with the program. Mathspig had a little play and produced the genetically challenged chicken (below).
The Pixar film, Finding Dory, began as storyboard sketches. There were 103,000 drawn for the film. The sketches are placed side-by-side in sequence in order to convey scenes and deliver a rough sense of how the story unfolds.
How many 64-page Exercise books would the story board take?
Only one side of the page of the 64-page exercise book would be used for storyboarding.
No. exercise books = 102,000/32=3,187.5
If put into flip Book form the story board sketches would produce a ‘rough’ version of the film.
Superman Vs Goku
………………………………………..
2. Ratio
If you are making a film about, say, Godzilla, you want him to be big. VERY BIG. But he has to share a screen with human characters.
If Godzilla is too big all the humans look like ants.
If he is too small … he looks like a toy TRex.
The Monster Maths:
Height: 355ft Godzilla’s towering height in the 2014 film—the tallest onscreen incarnation ever
Tail: 550ft 4in Total length of Godzilla’s spiked tail.
Volume: 90,000 tons Godzilla’s volume if filled with water
Teeth: 3.51ft Length from the root to the tips of Godzilla’s canine teeth
Teeth: 60 Teeth in Godzilla’s mouth
Roar: 3 miles. Approximate distance Godzilla’s roar reverberates. (100,000W Power of the 12-foot-high, 18-foot-wide speaker array from which the sound designers blasted Godzilla’s roar to record the sound in a “real world” context)
Feet: 58ft Total width of Godzilla’s feet across the widest point
Feet: 60ft Length of Godzilla’s footprint from toe to heel
You vs Godzilla
The average height for 14-year-old boys in the U.S. is 64.5 inches or 5 feet 4½ inches.
For 14-year-old girls in the U.S. the average height is 62.5 inches or 5 feet 2½ inches.
Godzilla = 355ft
14 yo =5’ 3”
Height:
355/5.25= 67.6 = 68
To make a 3D graph like this see below.
Footprint
You vs Godzilla’s Footprint
60/5.25 =11.4
Teeth
You vs Godzilla’s Tooth
3.5/5.25 = 0.7
………………………………………………
3. 3D Modeling: Polygon Count
3D modeling can be approached in several ways. There is a good explanation here.
One method is to use a 3D scanner to produce a 3D mesh.
Godzilla model under construction
Digital Godzilla as 3D mesh
The mesh consists of polygons. You’ll find everything you want to know about polygons here.
The greater the no. of polygons the better the resolution in a 3D mesh, the better theresolution of the character or object as more shading and texture variation can be added.
So the POLYGON COUNT or POLY COUNT is a measure of the quality of an image.
Here are some POLY COUNTS:
Godzilla
500,000 polygons.
It took the 4 CGI artists 6 months to fully nail the texture of Godzilla’s scales. (See above)
Elysium
Just the space station ran close to 3 trillion polygons.
Transformers 2
Devastator had 13 million polygons
Clash of the Titans
The Kraken had 7 million Polygons.
Avatar
Apart from some bluescreen shots of live-action actors in cockpits, it’s all CG: gunships, missiles, smoke trails, water, fire, an army of photorealistic virtual characters and a giant tree made of 20 million polygons with 1.2 million leaves.
The POLY COUNT is always greater in animated movies than in video games mainly because a higher poly count takes longer and costs more. A higher resolution is needed in a movie as it is shown on a much bigger screen.
Gollum: Game vs Film 3D model
Here are some POLY COUNTS for some popular games:
The Amazing Spiderman
Spiderman – 11,652
Assassin’s Creed 3
Benjamin Franklin – 17,744
Charles Lee – 25,994
Connor Kenway – 28,501
Desmond – 14,934
Haytham Kenya – 19,985
Batman: Arkham City
Batman: Film Version
Batman: Game Model
Batman Beyond suit – 13,050
Harley Quinn – 17,731
Harley Quinn (DLC) – 19,110
Poison Ivy – 15,977
Call of Duty: Black Ops
Frank Woods (full gear) – 19,777
Crysis 2 (console)
Nano suit – 19,073
Multiplayer suit – 27,414
………………….
FREE 3D MODELING FOR MIDDLESCHOOL STUDENTS
TINKERCAD is the free online resource that allows students to create their own 3D graphs – like Godzilla vs You (above) or 3D images that can be used for 3D printing. Play with the program. Mathspig had a little play and produced the genetically challenged chicken (below).
With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.
METRIC UNITS
Background Story
On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.
HOW FAST CAN YOU RUN?
METRIC UNITS
Time Trial:
Mark out a 10 m course. Make 3 time trials.
t1 =
t2 =
t3=
Average your time:
tav = (t1 + t2 + t3)/ 3 =
Your Speed S = 10/tav = ……… m/sec
HOW FAST IS A GRASS FIRE?
This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 20kph (up to 30 kph) in a gentle breeze.
Fire Front Speed Grass Fire
Fire Front Speed = 20 kph = 20 x1000/(60 x 60)
= 20 x 0.27777777 = 20 x 0.28 m/sec
= 5.6 m/sec
CAN YOU OUT RUN A FIRE?
Average Running Speed Boy 13–14 yo = 3.0 m/sec
Average Running Speed Girl 13–14 yo = 2.4 m/sec
We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.
This is not looking good. See more Firefighters Need Maths here.
We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions here.
NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?
We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.
Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:
High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.
The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.
What happened to the Smoke Jumpers?
When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?
ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.
With wildfires in Texas and now Australia is facing the fire season, it is time to think about fire fighter maths.
USA UNITS
Background Story
On 5th August 1949 Wag Dodge was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.
HOW FAST CAN YOU RUN?
USA UNITS
Time Trial:
Mark out a 30ft course. Make 3 time trials.
t1 =
t2 =
t3=
Average your time:
tav = (t1 + t2 + t3)/ 3 =
Your Speed S = 30/tav ft/sec
HOW FAST IS A GRASS FIRE?
This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at 12mph (up to 20mph) in a gentle breeze.
We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.
This is not looking good. See more Firefighters Need Maths here.
We can do very accurate calculations using simultaneous equations. Wildfire Algebra: Detailed Worksheet using simultaneous equations and solutions here.
NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?
We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.
Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:
Now you can calculate the distance travelled up a slope at a 30º angle.
Don’t forget you can use the WEB 2.0 Calculator here
Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that you cannot out run this fire front.
Again we can do very accurate calculations using simultaneous equations.
High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 70 mph and temperatures up to 2000 °C, which can and does melt glass and cars.
The fire front speed doubles with every 10º, so speeds for the fire front in a strong wind can reach 140 mph, 210 mph and up to 280 mph.
What happened to the Smoke Jumpers?
When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?
ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.
Mathspig has gone, like, totally Cubist this month. You too can turn any portrait of yourself into a Cubist Master piece (See Mathspig portrait above), here.
Mathspigs maths friends, Lyn and Erwin, who I met at the 13e Salon Culture & Jeux Mathematique, Paris, have sent me a reminder about their amazing Cryptocube construction kit (Mathspig is twirling one above) . This is not for the faint hearted. It’s a Big Maths challenge, but well worth the investment especially for schools. You can learn more about the Zometool Cryptocube construction kit here.
Meanwhile, here are links to 10 Amazing Ways to See a Cube:
You will find more interesting Fluid Geometry works by Clint Fulkerson here.
Hellooooooooo My Sweet Little Picassos,
