Here is the x-y graph for different launch angles.

trajectory wired magazine

You can go to this page for complete calculations. Aerial skiers twist and turn but their CENTRE OF GRAVITY must follow this graph. More on centre of Gravity at The Great Back Pack Attack ie.

The centre of gravity of Aerial Skiers must follow a

This response often results when students face some new topic – often beyond numbers – that students can’t handle on auto pilot. Instead of working through the problem, they crash and burn.

………………………………………………………………………….

The Solution:

I’m going to tell you a story. Bear with me for a minute. You did maths from Grade 1 to 6. You’re cool. No major dramas. Then something happens. A new topic, perhaps. Or a new teacher and a new topic. You don’t get it. You sit there looking confused. And then you do this. You say ‘I can’t do maths’( See post here) or ‘It’s too hard’.

In my maths teacher days terror topics were:

Long division

Algebra

Dividing Fractions

Geometry (because so few students listen to what the teacher is saying.)

Trigonometry (Lot of, you know, things to learn. Equations and stuff.)

So you stop doing maths. You retire at the age of, maybe, 13 years.

If you hit the MATHS WALL, here’s what you have to do. Back up a bit. Do some warm up maths on the topic. It’s out there.

eg. The Kahn Academy. I’m not saying it is easy. (See THE MATHS SPEECH here) I’m telling you it is doable. Practise.

Maths is always TOO HARD when you give up. But when you try amazing things can happen.

Besides, if a raccoon can do it.

Here is an exercise that you didn’t think you could do. But it is entirley doable by Middle School students with patience.

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 m^{3} 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

………………………………………………

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

………………….

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).

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 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

………………….

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).

Statistics for alcohol consumption are tricky. Binge drinking gets confused with heavy drinking. If you want to stay young go to the UK. They think anyone under 35 is a youth! Some stats separate Male and Female drinking habits. Some don’t. And legal drinking ages vary. Canada is one crazy place. It has different legal drinking ages in different parts of the country.

Legal Drinking Age:

The Maths

What we are working on here is reading maths data. No lectures. The numbers speak for themselves.

Alcohol related death stats over lap other stats including death involving cars, motorcycles, bicycles, skateboards, jet skis, quad bikes, drowning, diving, stairs, supermarket trolleys and evenhigh heels.

Under 18 years of age. 1996 It is believed that as many as 83 percent of teenagers in Canada consume alcohol. Back in 1996, underage drinking was responsible for 3,500 deaths and 2,000,000 injuries. A 2002 survey found that 20 percent of eight graders had consumed alcohol within the previous month. Source

4,358 people under age 21 die each year from alcohol-related car crashes, homicides, suicides, alcohol poisoning, and other injuries such as falls, burns, and drowning. Source

These countries have different populations (See post below). USA population is 15 times Australia’s. 260 x 15 = 3,900. So the Aussie and US stats are in the same ball park even though the stats have been collected for different age ranges. But look at Canada. The USA population is about 9 times Canada’s. 4,358 ÷ 9 = 484 deaths. This death statistic for Canada is 10 times larger than the USA statistic per head of population.Meanwhile, the population of Canada is 1 1/2 or 1.5 times Australia’s. 260 x 1.5 = 390. Once again, the Canadian statistic is out by a factor of 10. What’s going on here?

The Bar Where You’re Too Afraid to Get Smashed

Mathspig is a party pig. But why does anyone drink themselves senseless? Many reasons, but one is they’re bored. Now here is a bar in Mathspig’s home town, Melbourne, where you better stay sober.Break out of prison in Trapt Bar.You’re in prison, you’re innocent, and no one believes you. You plot an escape with the other prisoners–because unless you break free soon, you’ll all face an unspeakable death (this prison is off the charts). At Trapt Bar and Escape Rooms, you and your teammates have 45 minutes to find clues, solve puzzles and escape before…well…let’s spare you the gruesome details.

Pringles are mathematically yummy because each Pringle is a little 3D graph called a Hyperbolic Paraboloid or – YeeHa! – it’s a saddle.. You will find information about Hyperbolic Paraboloid at the fab Math Jokes 4 Mathy Folks bloghere and here.

You may have drawn 2D graphs. Bar graphs, Pie Charts and Linear Graphs.

A linear graph will have the equation

y = mx + c

You might have looked at quadratic equations such as the parabola:

Y = ax^{2 }+ bx + c

So what could a 3D graph of a saddle look like? Well, you have to add a z so that you have an x-axis, y-axis and a z-axis.

Can you make a hyperbolic paraboloid? The most mathematically amazing feature of the hyperbolic paraboloid is that it can be constructed from straight lines.