## 10 Amazing Ways to See a Cube

March 23, 2023

The CUBE GIF (above) is mesmerising. But there are many different ways to look at a cube.

Here are links to 10 Amazing Ways to See a Cube:

## 1. Tube Cube

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## 2. Folded Paper Cube

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## 3. Anamorphic Cube

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## 4. Floating Cube

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## 5. Street Art Cube

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## 6. EDIBLE CUBE

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## 7. GIANT CUBE

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## 8. Spaghetti Cube

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## 9. Fashion Cube

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March 18, 2022

## A COOL MIDDLE SCHOOL MATH EXERCISE

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.

x2 Tables on a Circle pdf file for printing

This circle graph blank could also be used for x3 and x4 tables, which produce totally different yet equally amazing patterns.

Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.

ie. 27 x 2 = 54, 28 x 2 = 56 and so on.

so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc

This shape is called a CARTIOID.

## Death by Caffeine: The Maths  Part 1 METRIC

November 26, 2021

Death by Caffeine: The Math  Part 1 USA UNITS here.

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.

## Death by Caffeine: The Math  Part 1 USA UNITS

November 26, 2021

Death by Caffeine: The Maths  Part 1 METRIC here

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.

## 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 Maths: 3D Animation … Metric units

July 4, 2020

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 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.

# 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: 1.07m  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

# 108.2/1.6 = 67.6 = 68

## Footprint

You vs Godzilla’s Footprint

# 18.18/160 =  11.4

## Teeth

You vs Godzilla’s Tooth

# Here is Superman vs Godzilla

A very funny Aussie commentary.

# 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.

## 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).

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!!!

## The Rolling Coin Paradox that drove me Crazy!

June 4, 2020

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)

## It is Xmas … Ah! The Joy of Algebra!

December 5, 2019

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.

## Make a Cool Pattern with x2 Tables… but it is trickier than you think.

September 6, 2019

## A COOL MIDDLE SCHOOL MATH EXERCISE

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.

x2 Tables on a Circle pdf file for printing

This circle graph blank could also be used for x3 and x4 tables, which produce totally different yet equally amazing patterns.

Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.

ie. 27 x 2 = 54, 28 x 2 = 56 and so on.

so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc

This shape is called a CARTIOID.

May 14, 2019

# Grizzly Bear

Weight:   250kg

Height:   250cm

Top Speed: 56kph  =   16 m/sec

More bear stats here.

# Brown Bear

Weight:  680kg

Height:   250cm

Top Speed: 35kph  = 10m/s

More bear stats here.

Comparing these speeds to the fastest man on earth, Usain Bolt:

# Usain Bolt:

Top speed: 243kph =   12m/s

So Usain Bolt could out run a Brown Bear but NOT a Grizzly!

# Bears are NOT as dangerous as:

In fact more Americans die choking on their own vomit each year than a re killed by bears.

More death stats here.

But bears are very fast so Park Rangers recommend the following survival tactics:

More bear survival info here.

REF: Dog helps save hikers after grizzly chases them for 20 minutes here.