Archive for the ‘Ratio’ Category

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The Rosetta Project … like throwing a dart from Sydney to Perth and hitting the bullseye

November 28, 2014

Many commentators in Australia claimed that the Philae landing was:

This is equivalent to hitting the bullseye of a dartboard in Perth from Sydney. With a billion euro ($1.4bn) dart. While blindfolded (as the mission was powered down for almost the entire journey). ABC The Drum

Did they get the maths right?

Inner bullseye of dartboard = 12.7 mm

1 Dartboard

67P comet = 4.1 km = 4,100 m at widest point

Distance comet from earth = 520 million km

 Actually, hitting the 67P comment was more like roulette as the Rosetta mothership swung into orbit. And, as the earth and the comet are moving, the distance constantly changes, but you can watch the distance changing here.

Fabulous Graphics from the Daily Telegraph

Fabulous Graphics from the Daily Telegraph

In the Dart Throwers Universe

We will assume someone can stand on earth and throw a dart at the comet … Yes! They would need very big triceps.

3  Dart throwers universe correction

 

So the commentators aren’t even close. It would still be a feat hitting a bullseye with a dart from 160km, but that would be from Sydney to, um, Nowra on the coast. 

WHY?

Comet vs bullseye ratio mathspig

Mt Everest RAtio

4 Dart Throwers universe 3

The distance from Sydney to Perth is 4100 km. At best the commentators would be talking about throwing a dart from Brisbane to Adelaide is 2044km (below).

Brisbane to Adealide

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3. How far can a bio-fuel Mini drive on 1 kg of human fat?

September 30, 2014

man vs mini 5b

Of course, in heavy traffic you are burning up the bio-fuel/fat getting nowhere.

Fuel Consumption (F) can plummet, even for the Mini, from 3.4 kg/ 100 km to 6.8 kg/100 km to 8.8 kg/100km. You may as well get out of the car and walk!!

ENERGY:

In Biodiesel

Consumed walking

In FAT including Human Fat

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Outdoor Maths Adventures: Grade 3 – 5

June 30, 2014

Outdoor Maths 1 Mathspig 2

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.

Outdoor Maths 2 Mathspig

Outdoor Maths 3 mathspig

Outdoor Maths 4 Mathspig

Outdoor Maths 5 Mathspig

Outdoor Maths 6 Mathspig

Outdoor Maths 7 Mathspig

Outdoor Maths 8  Mathspig

Check out Mathpig’s protractor joke here.

Outdoor Maths 9 Mathspig

Outdoor Maths 10 Mathspig

Another fab idea from Juliet Robertson.

 

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2. Make a 3D Mini Me

October 24, 2013

The UK supermarket chain, Asda, is currently trailing 3D in-store printing of mini-me figurines. Cost: £ 40  (€ 47 or $Aus 67 or $USA 64)

Customers can buy 3D coloured versions of any person or object including the family car or dog (if Trixy can keep still for 2 mins) scaled down to an 8-inch figure.

Picture 2

Now you too can play games with yourself. (Warning: Avoid wording involving ‘play with’ and ‘yourself’.)

It takes two minutes using a hand-held scanner to create the 3D image and 6 – 8 hours for the 3D printer to produce the figure.

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The Virtual You

3D body scanning already exists so you can create a 1:1 scale avatar (A Mevatar, perhaps?) of youself for online shopping. By combining this technology with 3D printing the scaled-down Mini Me concept was born.

YOu can walk your personal exact-scale Avatar into an online shop and try on clothes!

YOu can walk your personal exact-scale Avatar into an online shop and try on clothes!

3D PRINTING: THE MATHS

Maths is involved at every stage of the Mini Me production to produce the scanner, the scanner program, the printer and the printer program.

It is the scale that is intriguing.

The scale used by the 3D printer is approx 1:10 ratio.

What?

According to the BBC average man in England is 5ft 9in (175.3cm) tall and weighed 13.16 stone (83.6kg) and woman is 11 stone (70.2kg) and  5ft 3in tall (161.6cm).

3D printers use materials from brass to silver to ceramics so figurines can be quite heavy.  Assuming the ceramic material has a similar density to the human body, the 1:10 scale male figurine would weight over 1 stone (8 kg) and a female 1 stone plus (7 kg)!

Will shoppers be staggering home in York carrying 7kg figurines?????

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Wait a minute:

mini mathspig Me

1:10 scale along each axis produces an overall scale of 1:1,000
1:10 scale along each axis produces an overall scale of 1:1,000

10 by 10 cube

Mini Me Mathspig is just 1/1,000 of Big Mathspig

or one little cube in the pack of 1,000.

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The supermarket figurine @ 1:1,000 scale by volume (and, assuming, weight too) would weight 83 gm ( 3 ounces) for men and 70 gm (2.5 ounces)  for women. That’s more like it. The figurines will be, in fact, a little heavier as customers will be scanned wearing clothes and shoes, we hope, or the scanning sessions at the supermarket will be really weird.

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What next?

How about your face on a Star Trek Figurine?

Done. See Engadget.

Yes, mathpiggies, we want maths to boldly go where no maths has gone before ……

Star Trek pic

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5 Wrangle an Orderly Tangle

April 9, 2013

Maths-is-Awesome Activity

Wrangle an Orderly Tangle

Skill: Geometry, scale, ratio, measurement

Level: Junior & Middle School

100.1 Justin Meyer math-craft-monday-community-submissions-plus-make-orderly-tangle-triangles.w654

100.2 math-craft-monday-community-submissions-plus-make-orderly-tangle-triangles.w654

There are some wonderful projects at Mathscraft. But one students of any age will enjoy is creating an orderly tangle of triangles below. You can find a PDF template download for thise triangles @ the Mathscraft link above.

100.3 math-craft-monday-community-submissions-plus-make-orderly-tangle-triangles.w654

And this Orderly Tangle of 4 Triangles can be made on any scale from cute earrings to ORDERLY MONSTER TANGLE. Go wild mathspiggies.

math-craft-monday-community-submissions-plus-make-orderly-tangle-triangles.w654

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Lego Olympics Flags

February 23, 2012

The Lego Marching band is rehearsing for the Opening ceremony.

Lego Olympics 2016

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………….Bandito (Republic of Baddies)

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Mr Boopy (Bozonia)

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Gorilla Suit Guy (Halloweenotopia)

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………………..Barry the Butcher (Alien Steakistan)

……………..BioHaz (Toxorama)

…………………Dead-Eye Doc (AyeAwArghia)

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Dr Jabb (Bummerville)

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Hula Lula (Grinmania) 

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1. Flag Fractions

EQUIPMENT: Mixed Lego Blocks

Here is the maths. It’s fractions. It’s simple.

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A. National Flag of  Comotosia

They’re a bit sleepy in Comotosia so you better design a flag to wake them up, mathspigs.

The flag must measure ………….   6 blocks x  12 blocks.

One block is a 4 bumps blocks (See pic). An 8 bumps block equals 2 blocks.

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Here’s the catch, mathpiggies.  1/4 of the blocks in the flag must be RED.

How will you do this? (Hint below)

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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.B. National Flag of Bordom

Once again the Bordonians need a lively flag.

The flag must measure 6 blocks by 12 blocks, but this time it must contain 1/4 red and 1/3 blue. How do you do this?

Hint: Mathspigs! You will have to count the number of red and blue blocks.

 

2. Design A National Flag to Lego Scale

First, name your Lego man, girl or alien and pick a name for their country, planet or crypt.

You will be drawing two flags.

All national flags are rectangles except Switzerland and Tibet, which have square flags but not at the Olympic Games.

Olympic Flags measure:  150 cm x 90 cm

or …………………………….. 60 inches x 35 inches.

These sizes are not equal so which flag is bigger the decimal flag or the Imperial Units flag?

The Imperial units flag is 152.9 cm x 88.9 cm. It turns out the area of the Decimal flag is 13,500 cm2 and the Imperial Flag 13,593 cm2

You will be designing a decimal flag.

Note the Flag ratio of length: width = 150 : 90

…………………………………………………… =  15 : 9 = 5: 3

First design a flag with 5: 3 ratio.  One measuring 10cm x 6 cm would be ideal.

 

BUT

How big are the national flags at the Lego Olympics:

Real flags at the Olympics =  150 x 90 cm

Lego Flag measurements =  150/50 x 90/50 = 3 cm x 1.8 cm = 30mm x 18 mm

Here are my two Lego people with flags  I prepared earlier:

The Enforcer from the Constellation of Obeymia and Mr Boopy from Bozonia.