## Posts Tagged ‘Graph’

## 5. It’s Too Hard

September 29, 2017## 1. Middle School Madness: BIG MATHS

June 12, 2017Community Maths can involve the school community or the wider, local community. The aim is to get maths out of the classroom and make it a hands-on experience.

Set up displays, posters, demonstrations or art/maths projects in your school library, gym or school yard or take some interesting maths to the local library, strip mall, town hall, local gardens or shopping mall. It will mean planning the project, collecting the materials and making a phone call to the local, say, librarian, but libraries, for instance, welcome community involvement.

Here are just some community maths project ideas.

# MATHS POSTERS

Major maths conferences around the world have **poster displays**. So why not a display of students maths posters in your school library or local library or even a nearby shopping mall. And students should be present at allocated times to explain their poster to other students, parents or members of the public.

Roosevelt Middle School students Jacob Klausner and Oliver Adelson WEST ORANGE, NJ, who were finalists heading to the **National MathCon Competition.**

Some of the best middle school maths posters can be found at **MathsCareers**, UK. Here are some posters from the 2016 competitions.

Winner 9 – 11 years Maths Poster Competition

Fatimah Patel Preston Girls High School

Runner Up 9 – 11 years Maths Poster Competition

Maja Kowalska McAuley Catholic High School

Winner 12-13 years Maths and Music Poster Competition

Laeticia Junanto Bancrofts School

# MATHS DEMONSTRATIONS

Maths students can construct displays that involve interesting maths. The most amazing maths dispalys Mathspig has seen were at the 13e Salon Culture & Jeux Mathematique in Paris. Here is LAGA Phd student Attouchi @ the** 13e Salon Culture & Jeux Mathematique in Paris.**

She was showing students how to use a graph to create anamorphic projections. More detailed instructions **here!!!**

Palestinian Maths teacher Daina Taimina has many zany ideas. You’ll more Creative Maths ideas** here.**

Mentalist Maths … OK. This may include some Card Tricks … but they’re amazing. You’ll find 10 amazing Mentalist Math Tricks **here**.

Make some interesting cubes** here.**

Give students a variety of maths challenges they have to solve

like these Maths Mystery Box Challenges **here.**

Or let students explore some of the inspiring maths websites and pick a project. You will love the amazing German website **IMAGINARY**. It’s in English and has some fascinating videos!!!!!

Perhaps students could construct double pendulum like this one demonstrated at the MiMa-Museum, Oberwolfach, Germany. Mathspig can’t stop watching it. Fascinating!!!!!!! The double pendulum has some demanding trigonometry, but at the middle school level the 2D graph traced by the lower pendulum is fascinating enough (Below). And maths can provide equations for this movement. That’s impressive.

## 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!!!

## 3. Anamorphic Cube

February 11, 2016**This is quite a challenge. The idea is to draw an anamorphic cube so that the image, once projected onto a curved surface looks like a cube. You will find the template or graph for this exercise on Mathspig here. **

**It took me several goes to get it … sort of … right.**

**Step 1: Make silver foil/cardboard cylinder to fit the dotted circle on the grid below.**

**Step 2: Draw in the corners of the cube on the square grid and match these corners on the curved grid.
**

**Step 3: Draw in the three vertical sides of the cube and match these lines on the curved grid.
**

**Step 4: Draw in the top and bottom horizontal sides of the cube on the square grid and match these on the curved grid.
**

**Getting tricky now.**

**Step 5: Draw in the blue, orange and green sides of the cube on the square grid and match these on the curved grid.
**

**Step 6: Place silver cylinder on dotted circle.
**

**Step 7: Can you see the cube?**

**Step 8: Here’s a closer look.**

**An even better Anamorphic Cube.**

**Anamorphic Illusion Art of a Rubik’s Cube**

**By John Snow**

**Amazing Anamorphic Illusions by Brusspup**

## Lego Mean, Median, Mode

January 15, 2016Students can calculate the Mean, Median and Mode using Lego. Here is the exciting part:

The lego stacks become the graph

# START with 40 LEGO BRICKS

Draw a graph of No. of Blocks Vs No. of Prongs (per block) Make sure all blocks are the same height.

Start with 40 bricks.

Sort into Stacks to create graph of

No. Prongs Vs No. Bricks

This is a close up of the stacks above.

The no. of bricks in each stack is written on top of the stack.

## Death by Chocolate: The Maths

May 28, 2014#### Choco Yum Yum! Mathspig lervs chocolate. But did you know chocolate can kill you?

#### Chocolate contains a chemical called Theobromine. This alkaloid ( other alkaloids include cocaine, nicotine, caffeine and strychnine) can kill humans. More info Wired Magazine.

# How much chocolate is too much?

#### Firstly, the darker the chocolate the more Theobromine it contains.

#### According to About Chemistry:

#### Based on highest possible toxicity:

White Chocolate: insignificant

#### .

#### .

## Milk Chocolate 1-5 g/kg

#### 200gm block = 1 gm per block

……………………………………………………………………………………….

## Dark Chocolate 10 g/kg

#### 200gm block = 2gm per block

#### ..

…………………………………………………….