## Archive for the ‘Ratio’ Category

## The Lego Olympics 2020

July 30, 2021## Toilet Paper FUN FACTS Maths

June 1, 2021Mathspig is in Melbourne, Australia. We’re in Lockdown. AGAIN!

And toilet paper has disappeared off the supermarket shelves. AGAIN.

So today we are doing maths based entirely on toilet paper using information from the Toilet Paper Fun Facts website. Yes! It exists **here**.

**Toilet Paper Fun Facts Website**

**Protractor Wind Speed Calculator**

**POP UP ANS Q 1 & 2 Yr 7&8 Toilet Paper fun facts**

**Pythagoras Equation Diagram here**

**Here is the Sine Rule (Watch 1.5 mins)**

**Check sine curve here:**

**Listen to sine curve here:**

## King Kong Power Punch 2021 USA units

January 30, 2021## Make A Maths FACE Mask

July 21, 2020**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**.

## ZOOM Math: 3D Animation …. USA units

July 4, 2020Middle 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 in **TINKERCAD**. (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

# ………………………………………..

# 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: 3.51 ft 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 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:

## 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.

More **here****.**

## Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

# Film Animation vs Game Animation

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 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).

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!!!

## Outdoor Math Adventures: Grade 3 – 5

September 12, 2019It’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.**

** **

## Stunning Art based on Maths

September 29, 2018Adam 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.

# What fibonacci art can your class make today?

You can find more of Adam’s inspiring maths art works** here**.

## CGI and Middle School Maths … Metric units

April 9, 2017# 1. Story Board 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 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: 1.07m 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

# 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 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:

## 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.

More here.

## Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

# Film Animation vs Game Animation

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).

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!!!

## CGI and Middle School Math …. USA units

April 9, 2017# 1. Story Board 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 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 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:

## 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.

More here.

## Lord of the Rings – The Two Towers (2002)

(See below)

The Gollum head model consisted of just over 2,600 polygons, which were mostly quads.

More here.

# Film Animation vs Game Animation

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).

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!!!