Melbourne singer, songwriter, and geometrically inclined performer Gotye performing with Kimbra won 3 Grammy Awards for his song Somebody that I used to Know in 2013.
The Gotye youtube clip has had 1,535,344,012 or 1.5 Billion hits since it was first uploaded 5th July 2011.
Mini Rates Exercise:
In 111 months Somebody that I used to know has scored 1.5 Billion hits. How many hits a. per month, b. per day, c. per minute? (Round off numbers)
Ans: a. 13.5 Million per month
b. 450,000 per day (Assuming 30 days per month)
c. 37,500 per hour and 625 per minute (for over 9 years non stop!)
Estimate of Youtube Earnings for this Song:
The Influencer Marketing Hub puts the rates an advertiser pays between $0.10 to $0.30 per view on Youtube, but averages out at $0.18 per view. Using the lower rate, how much has this song earnt in just over 7 years?
Earnings = 0.10 x 1.5 x 109 = 1.5 x 108 = $150,000,000 = $150 million*
*This calculation is based on a click per view of the video. Gotye will not receive anything like $150M, however, because advertisers pay per click on their ad.
According to the Influencer Marketing Hub again ‘on average, the YouTube channel can receive $18 per 1,000 ad views. This equates to $3 – $5 per 1000 video views.’ Again, using the lower rate:
Video Hits =1.5 x 109
Divide by 1,000 = 1.5 x 109 ÷103 = 1.5 x 106
$3.00 per 1,000 video clicks earnings = 3.00 x 1.5 x 106 = 4.5 x 106
Realistic Earnings = 4.5 x 106 = $4,500,000 = $4.5 million
A Geometric Parody:
Here is Mathspig’s take on the song:
Somebody that I used to Know:
It’ll either help students do their exercises or work like Clockwork Orange and have them running screaming out of the room when they hear the first few notes.
The NHS reports that Australian Researchers Declan Patton and Andrew McIntosh, Uni of NSW, have conducted a study into brain and neck injuries of headbangers published in the British Medical Journal.
Concerts included as part of the study included Motörhead, Mötley Crüe, Skid Row, The Hell City Glamours, L.A. Guns, Ozzy Osbourne, Winger, Ratt, Whitesnake, and W.A.S.P.
Here’s Motorhead with a ‘nice’ moshpit.
140 BPM for Ace of Spades. Motorhead BPM range is 91 – 203
The Headbanger Study Concluded:
1. Head movement of more than 75o for an average heavy metal beat will cause head and neck injuries. This movement causes headache and dizziness.
2. Beats above 130 bpm (beats per minute) cause neck injury.
The average headbanging song has a tempo of about 146 beats per minute (bpm).
and according to Mathspig:
3. Being punched up in the mosh pit. Do you need maths for that conclusion?
Researchers recommendations:
1. Reduce range of head and neck movement
2. Headbang to a slower tempo
3. Wear a neck brace. (Isn’t a bad hair cut enough?)
Headbanger Rates Exercise:
How many headbeats per song of 5mins would a headbanger manage for the following song tempos?
Mathspigs excited. Look there is a band called Mutemath!!!!!!!! And here they are:
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Just to show that there is something spookily primitive about headbanging here is Headbanger Baby:
Boredomaccounts for nearly a third of the variation in student achievement.
Half of high school dropouts citeboredomas their primary motivator for leaving.
Boredom begins for Math students at Grade 6 when students (Common Core Standards, USA) tackle more abstract concepts such as linear eqns, exponents, probability, geometry and so on.
Math curriculums in the USA, UK & Australia all demand students solve REAL LIFE problems. Too often these are of the type:
Q. Ronaldo has tethered his goat on a 12ft rein in the corner of a 20ft square field. What area can the goat graze?
THE ANS: Who cares?
Simple.
Ask students maths questions which have answers they want to know.
Students really don’t care about Ronaldo’s goat, but here are some questions which involve intriguing answers they might want to work out. And many of these questions involve funny or age-relevant activities, which also helps engagement.
The average time it takes an audience at a conference to switch off is 11 minutes. Keep in mind this audience is, at least, being paid to be bored witless.
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.
“With enough stupidity you can get any car to roll over” (MSN AUTO)
What stuntmen and women need is maths!
Maths is essential to the process, from calculating speeds and braking distances to looking at the ratio of the amount of film shot to the length of time of the end sequence. The stunt and crash is outlined, and the co-ordinator explains how he must calculate speeds and stopping distances carefully.
So you want to be a stuntman?
First think of the pain.
Mark Eiden, 52, a professional stuntman (pictured) who is not only afraid of heights, but was once told he likely wouldn’t walk again. Eiden’s had surgery on both arms and shoulders, five knee surgeries, six nasal reconstructions, foot and hand surgery and a facial cast. He fell off the top of a stunt car at 40 mph when the tyre blew. He gaffer taped his ear and continued, despite severe concussion. Northern Express Michigan
If you still want to be a stuntman do the Maths:
Rolling a Car:
You can use quick handbrake turn, speed around a corner, fishtail into the curb or some other lunatic thing. The most controlled way to roll a car is to use a ramp.
These ramps often have a kicker at the end to add extra lift. Ramp calculations can be complicated, but the simplest way to look at the maths is to determine the angle a car will roll ie. When the Centre of Gravity moves over the base.
Centre of Gravity vs Base Width
The distance between the front wheels in cars is often called the track width.
So the Lamobgini Diablo is very hard to roll (build a higher ramp) and it therefore beats the SUV for stability every time.
Balancing on 2 Wheels
A more skilled stunt involves driving a car on two wheels. A very skilled stunt driver can lift the car onto wheels by snaking the car back and forth across the road until it balances on 2 wheels.
From the Centre of Gravity vs Base angles above you can see that the SUV is the easiest car to balance of 2 wheels.
But there is nothing quite as crazy as this SUV stunt:
Star Stuntman Monte Perin (pictured) has involved many films, including “Spider-Man,” “Star Trek, “Indiana Jones and the Kingdom of the Crystal Skull” and portraying Arnold Schwarzenegger’s stunt double in “Terminator 3: Rise of the Machines.”
Perhaps his most difficult stunt was landing his Harley in an open boxcar of a moving train for Disney’s 2008 Adam Sandler movie “Bedtime Stories”. In a career of over 25 years Perin has broken “almost everything” including both his arms, legs, knees, feet, ankles, several ribs, his back and his pelvis. See Confessions of a stuntman
Veteran stuntman Evel Knievel (1938 – 2007) was the pioneer of many stunt jumps. Here he is jumping 10 cars and 3 vans in 1973.
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
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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).
Mathspig Blog 
