Archive for the ‘Ratio’ Category

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CGI and Middle School Maths … Metric units

April 9, 2017

1. Story Board Sketches

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: 1.07m  Length 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: 17.66m  Total 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 the  resolution 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.

More here.

Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

Film Animation vs Game Animation

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).

Tinkercad Dashboard

Find here.

Drag and drop shapes.

More here.

Play with shape dimensions.

More here.

Create figures for 3D printer.

MATHSPIG REPORT CARD: More playing with program needed!!!

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CGI and Middle School Math …. USA units

April 9, 2017

1. Story Board Sketches

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 the  resolution 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.

More here.

Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

Film Animation vs Game Animation

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).

Tinkercad Dashboard

Find here.

Drag and drop shapes.

More here.

Play with shape dimensions.

More here.

Create figures for 3D printer.

MATHSPIG REPORT CARD: More playing with program needed!!!

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Dangerous Maths 2: Death by Snake, Spider, Quad bike, Kangaroo, Raccoon and Vomit

August 7, 2015

This post is really a PR exercise for sharks. We fear them. We’re horrified by the thought of being eaten alive!!!. We only have to hear the sound track from JAWS to feel the fear.

Why do we fear sharks? Look at the numbers. REALLY. Show your students. What about stairs??? Quad bikes? Chairs? Bees? That’s when you should feel the fear!!! We are irrational beings. This is why we need maths. We can make rational decisions using maths. There is also a safety message here. The maths speaks for itself. We won’t hammer it.

THE MATHS:

There is lots of maths you can do with these tables.

  • Bar Graphs
  • Pie Charts
  • Ratios (What’s the ratio of death by Snake to Quad Bike?)
  • Fractions (Show death by jet ski to falling down stairs as a fraction)
  • Percentages
  • Powers to the base 10. How many deaths occur in each country per 100,000 or 1 x 10head of population for, say, Quad bikes or ATVs? We can use these numbers to compare death rates and find out how dangerous riding a Quad bike is in each country.

……..Population Data

……..Aust…23 million = 23 x 106

……..USA…319 million = 319 x 106

……..Canada…35 million = 35 x 106

……..UK…64 million = 64 x 106

But we’re doing this for the SHARKS!!! Death Australia Mathspig

  1. Cyclists. 2. emergency lanes 3. fell off a chair 4.QUAD BIKES. 5. Horse, donkey. 6. buses 7. Cow, bull. 8. ice skates, skis or skateboards. 9. Venemous snake 10. kangaroo 11. bee 12. emu 13. Jet ski 14. Shark 15. Crocodile

Death USA Mathspig 21. Quad Bike or ATV: In 2007, 107 children younger than 16 were killed on ATVs. 2. Cyclists 3. choke on vomit  4. Cats, cows, horses, pigs, raccoons. 5. Bees, wasps  6.PWC or Jet Ski 7. Lightning 8. Xmas tree fires 9. Snowboard 10. Venomous Spider  11. Scorpions 12. Venomous Snakes , lizards. 13.Crocs & gators  14. Shark Death Canada Mathspig

  1. ATV Quad Bike 2. Canoe  3. Kayak 4. PWC or Jet Ski  5. Unpowered inflatable 6. Avalanches or landslides. 7. Lightning 8. Toboggan 9. Moose –Car collision 10. Bears (All Nth America) 11. Rattle Snake 12. Wolves 13. Shark

Death UK Mathspig

  1. falling down stairs.  2. Cyclists.  3. Choke on vomit   4. Falling off Chairs 5.  QUAD BIKE or ATV 6. Buses 7. Struck by cow, horse, other mammal 8. hornets, wasps, bees. 9. PWC or jet ski .10. Parachutists. 11. Skateboards, ice skates, skis 12. Canoe. 13. Shark 
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The Rosetta Project scaled down to a Lego Universe

November 28, 2014

According to Warwick Holmes, ESA:

The images were taken by the OSIRIS-Narrow-Angle-Camera on-board Rosetta spacecraft orbiting 15.5km above the surface of Comet-67P. They show the Philae trajectory before and after the first touchdown, which occurred at 15:34 GMT (12 Nov).  As previously reported the harpoons did not fire into the comet to hold Philae down.

The small inserted images show the imprint of the three Philae foot-pads left in the dusty surface of the comet (compare “before” 15:23 image and the “after” images at 15:43)  Philae first touchdown was at 15:34 GMT.

1 OSIRIS_spots_Philae_drifting_across_the_comet  2
Philae bounced off the comet surface after the first touchdown and remained “airborne” for 1hr 50min.  The first bounce was 1km high and went 1km directly east on this image.

Philae then touched down a second time resulting in a much smaller second bounce which lasted only 7 minutes.  The gravitational force on the surface of Comet-67P is 1/50,000th of (“g”) Earth’s gravity, hence the very high and long re-bounds.

This image does not show the second or final third touchdown positions as they were outside the field of view of this image as Philae continued heading east with respect to this image.
1a Rosetta lander on comet

Finally, Philae completed 100% of the science data acquisition sequence that was planned on the surface despite the “rough” landing(s).  It will probably be several months before exact scientific findings are being published as the scientists shall be spending many weeks processing and examining the plethora of scientific data from Philae and Rosetta over the landing site.

 This is fabulous. Live Comet up date here

To appreciate the distances involved we will scale everything down to the

Lego Universe:

2 Lego Space Cadet Human Ratio Mathspig

3 Lego Scale philae and comet

4 Lego Universe 1 mathspig

5 Lego Universe 2  Mathspig More Rosetta data from Warwick Holmes, ESA.

6 Rosetta Data

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The Rosetta Project … like throwing a dart from Sydney to Perth and hitting the bullseye

November 28, 2014

Many commentators in Australia claimed that the Philae landing was:

This is equivalent to hitting the bullseye of a dartboard in Perth from Sydney. With a billion euro ($1.4bn) dart. While blindfolded (as the mission was powered down for almost the entire journey). ABC The Drum

Did they get the maths right?

Inner bullseye of dartboard = 12.7 mm

1 Dartboard

67P comet = 4.1 km = 4,100 m at widest point

Distance comet from earth = 520 million km

 Actually, hitting the 67P comment was more like roulette as the Rosetta mothership swung into orbit. And, as the earth and the comet are moving, the distance constantly changes, but you can watch the distance changing here.

Fabulous Graphics from the Daily Telegraph

Fabulous Graphics from the Daily Telegraph

In the Dart Throwers Universe

We will assume someone can stand on earth and throw a dart at the comet … Yes! They would need very big triceps.

3  Dart throwers universe correction

 

So the commentators aren’t even close. It would still be a feat hitting a bullseye with a dart from 160km, but that would be from Sydney to, um, Nowra on the coast. 

WHY?

Comet vs bullseye ratio mathspig

Mt Everest RAtio

4 Dart Throwers universe 3

The distance from Sydney to Perth is 4100 km. At best the commentators would be talking about throwing a dart from Brisbane to Adelaide is 2044km (below).

Brisbane to Adealide

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3. How far can a bio-fuel Mini drive on 1 kg of human fat?

September 30, 2014

man vs mini 5b

Of course, in heavy traffic you are burning up the bio-fuel/fat getting nowhere.

Fuel Consumption (F) can plummet, even for the Mini, from 3.4 kg/ 100 km to 6.8 kg/100 km to 8.8 kg/100km. You may as well get out of the car and walk!!

ENERGY:

In Biodiesel

Consumed walking

In FAT including Human Fat

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Outdoor Maths Adventures: Grade 3 – 5

June 30, 2014

Outdoor Maths 1 Mathspig 2

This fab idea comes from Juliet Robertson, an outdoor education consultant in Scotland. Her blog Creative star learning is one of the most inspiring outdoor maths blogs you will find.

Outdoor Maths 2 Mathspig

Outdoor Maths 3 mathspig

Outdoor Maths 4 Mathspig

Outdoor Maths 5 Mathspig

Outdoor Maths 6 Mathspig

Outdoor Maths 7 Mathspig

Outdoor Maths 8  Mathspig

Check out Mathpig’s protractor joke here.

Outdoor Maths 9 Mathspig

Outdoor Maths 10 Mathspig

Another fab idea from Juliet Robertson.