This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.
Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.
And then watch the MATHOLOGER video for a really interesting explanation.
The lethal dose for caffeine is about 150 milligrams per kg of body weight. While the average person’s caffeine consumption is around 200 milligrams a day, the Mayo Clinic advises against exceeding 500 to 600 milligrams per day.
This work titled Timing is Everything is by street artist ABOVE in London.
You may want this much energy but be warned, energy drinks can kill.
It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 48 kg. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal.
See Death by Caffeine: The Maths Part 2 METRIC
Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.
The lethal dose for caffeine is about 68 milligrams per lb of body weight. Average consumption of caffeine is about 200 milligrams a day. The Mayo Clinic advises against exceeding 500 to 600 milligrams per day.
This work titled Timing is Everything is by street artist ABOVE in London.
You may want this much energy but be warned, energy drinks can kill.
It would take a ridiculously huge number of ANGRY WOMBAT energy drinks to kill a 14 year old weighing, say, 110 lb. Nevertheless, some kids are more sensitive to caffeine than others and then much lower levels of consumption of energy drinks can be fatal.
See Death by Caffeine:The Math Part 2 USA UNITS
Here is the work (see below) TIMING IS EVERYTHING by street artist ABOVE in London showing the timing.
MATERIALS: Sheet of paper (eg. A4), ruler, scissors & coloured felt pens.
I am using an Aranea Black Mask Design. We are going to design and make a MATHS MASK PATTERN. If you want to make one out of fabric you will find all the necessary instructions here.
Middle school students around the world have been learning maths via Zoom. ZOOM needs computers & WIFI. There are so many resources online but I cannot over-emphasise the amazing 3D skills developed just by playing with objects inTINKERCAD. (See logo above. More info below) Anyone who wants to work developing video games or animated films has to understand the logic and maths of 3D. Read on. And it is more challenging than you might think.
1. Storyboard 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 storyboard 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 storyboard 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
Here is Superman vs Godzilla
A very funny Aussie commentary.
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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 MIDDLE SCHOOL 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 MindYourDecisions blog (Video below) presents the PARADOX beautifully.
Now consider the example of the coin rolling around a coin of the same size. Intuitively we think …’OK. Same circumference, so the coin will rotate once as it rolls around a same-size coin. But this doesn’t happen. It rotates twice.
TWICE!
This observation is SOOOOOOOO counterintuitive we have to know why?…
Why?
Mr. MindYourDecisions doesn’t explain why this happens. The answer is interesting. The relevant point in the ROLLING COIN PARADOX is the centre of the rolling coin. The rolling coin rotates about that point. And that centre (the red dot in the gif below) moves through a circle twice the circumference of the stationary coin. It is much easier to understand when you see it. (Below)
Great Math Xmas Ornament Ideas for Middle School here @ MathEqualsLove blog.
Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.
This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.
Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.
And then watch the MATHOLOGER video for a really interesting explanation.
Mathspig Blog 