Mathspig loves this ‘Street Art’ time lapse clip made by projective geometry students at the Technical University, Munich.
SO … thought Mathspig … lets do it! Two days later Mathspig’s eyes nearly crossed trying to locate the Vanishing Point (below), which helps artists draw 3D images. It didn’t work due to the angle of elevation of the camera.
SO .. rethink needed. (See project 1 & 2 below)
Maths Meets Street Art:
Project 1
Students can draw this ‘hole in the earth’ by Circle/Line Art School on paper fairly quickly. The aim here is to practice 3D street Art.
Maths Meets Street Art:
Project 2: The BIG ONE
Students can draw this ‘concrete hole’ by MiltonCor on paper using a ruler, set square and pencils. Then they have to scale it up to a size large enough for them to sit on the steps. The class can the ‘concrete hole’ in chalk in the school yard. Basic shading only is required, not the shading detail shown in this video.
Finally, students can take a photo of themselves sitting on the ‘steps’ with maths books beside them.
Here is the AMAZING thing … according to designer Tom Wujec, who gives the TED lecture (below), the most successful tower builders are not business school graduates or CEOs, but kindergarten students. The stats are in the video. So here is the challenge. Can you build a structure higher than the towers built by kindergarten kids?
Towers built by Kindergarten Kids AVERAGE HEIGHT = 71 CM or 28 INCH
HIGHEST TOWER from 70 challenges = 99 CM or 39 INCH
The Tom Wujec TED talk is aimed at business ‘team building’. Nevertheless, it is an interesting challenge and fun too.
TAKE 2:
In fact, the Marshmallow Tower has been around for a very long time. This challenge for middle school kids involves as many marshmallows and sticks of spaghetti needed to build the biggest tower. This is also a great end of year/semester/week challenge.
Mathspig posted this picture of an awesome marshmallow tower here.
The maths that proves that the 45 degree angle is the angle that produces the maximum distance travelled is quite tricky and involves trigonometry. But this just shows how cool maths can be. See the full calculations here.
Here are some worksheets on MEAN, MEDIAN and MODE for middle school students. It also involves work with units (Metric/USA). But these are real numbers and the distances that 14 year olds can spit watermelon seeds is amaaaazing!
You can find the free pdf worksheets (included below) here.
Other fun middle school math(s) worksheets in the Hot Heels series at TpT include Unit Rates, Angles, Ratios and Algebra.
Ask volunteers to see how far they can spit a seed. (WARNING: The volunteer must breath in through their nose before they spit. You don’t want them inhaling a seed.)
You can find the free pdf worksheet (included below) here.
Other fun middle school math(s) worksheets in the Hot Heels series at TpT include
Unit Rates, Angles, Ratios and Algebra.
There is a lot of maths and science behind coffee sloshing in a coffee mug. ‘The human stride has almost exactly the right frequency to drive the natural oscillations of coffee’ explains fluid physicists at the University of California at Santa Barbara. You will find their full explanation 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
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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
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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
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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).
