It’s Autumn in UK & FALL in the USA so it’s the perfect time for a little bit of outdoor math for Grade 3-5 with AUTUMN leaves. Of course, you don’t need FALL LEAVES for this exercise, but it is colorful.
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.
Check out Mathpig’s protractor joke here.
Another fab idea from Juliet Robertson.
Adam R McCausland is a Belfast-based graphic designer whose stunning works incorporate maths themes.
Here is his work (below) titled Fibonacci / Poinsettia
This work (below) is titled: At theHeart of it all. I’ve never seen mirrored Fibonacci curve before. Fascinating.
You can find more of Adam’s inspiring maths art works 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.
If put into flip Book form the story board sketches would produce a ‘rough’ version of the film.
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.
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
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
You vs Godzilla’s Footprint
You vs Godzilla’s Tooth
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:
500,000 polygons.
It took the 4 CGI artists 6 months to fully nail the texture of Godzilla’s scales. (See above)
Just the space station ran close to 3 trillion polygons.
Devastator had 13 million polygons
The Kraken had 7 million Polygons.
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.
(See below)
The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.
More here.
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
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!!!
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.
If put into flip Book form the story board sketches would produce a ‘rough’ version of the film.
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.
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
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”
To make a 3D graph like this see below.
You vs Godzilla’s Footprint
You vs Godzilla’s Tooth
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:
500,000 polygons.
It took the 4 CGI artists 6 months to fully nail the texture of Godzilla’s scales. (See above)
Just the space station ran close to 3 trillion polygons.
Devastator had 13 million polygons
The Kraken had 7 million Polygons.
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.
(See below)
The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.
More here.
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
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!!!
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.
There is lots of maths you can do with these tables.
……..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!!! 
1. 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 
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.
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.
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
More Rosetta data from Warwick Holmes, ESA.
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
Inner bullseye of dartboard = 12.7 mm
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
We will assume someone can stand on earth and throw a dart at the comet … Yes! They would need very big triceps.
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.
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).
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.
Check out Mathpig’s protractor joke here.
Another fab idea from Juliet Robertson.
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Comic & cutting comment plus random raves.
