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# The Golden Ratio webquest project

This project is your final task in your geometry class. You will have until the end of the semester to complete it.

Your final product should be one of the following:
❏ An 8-page booklet made from a large supermarket brown paper bag... an 8-mega-page I-Pad
❏ A large poster
❏ A powerpoint-type presentation

The Golden Ratio is one of those math ideas that just goes on and on. It has fascinated not just mathematicians for centuries, but also philosophers, artists, theologians and a few pure cranks. It is surrounded with myths and mysteries as well as fascinating links to science, biology, art, architecture, astronomy...

What do I need to do?

Your job is to explore the ideas of the Golden Ratio and Fibonacci's sequence and see where they take you. This is an exploration.

You should read through the suggestions below, and find some web sites about the Golden Ratio. Once you are familiar with the basic idea of the Golden Ratio and how it relates to other ideas, you should research more deeply one or two particular points that interest you about the Golden Ratio for your booklet, poster or presentation.

Where should I start?

Some ideas where you could start your webquest include (in no particular order):

☞ Fibonacci's sequence and the Golden Ratio.

☞ How to find the Golden ratio from the Golden Rectangle.

☞ Myths of the Golden Ratio.

☞ The Golden Ratio in art (and no, the Mona Lisa is not based on the ratio...)

☞ Where's the ratio in a pentagon or pentagram?

☞ The Golden Ration in the movies or thriller novels.

☞ The Golden Ratio and snails.

☞ The Golden Ratio and the Fibonacci spiral.

☞ Leonardo DaVinci and the Golden Ratio (high myth warning!)

☞ How do plants and trees use the Golden Angle to make the most of the sun?

☞ How to calculate the Golden Ratio using algebra.

☞ The Fibonacci numbers in Pascal's triangle.

☞ Fibonacci and the Golden Ratio at the vegetable market and in the garden.

☞ Are the Golden Ratio and the Fibonacci numbers reflected in human proportions?

☞ The Golden ratio and the Egyptian pyramids.

☞ Lucas numbers... what are they?

☞ Is there a Golden Triangle?

☞ What's special about the reciprocal of the Golden Ratio?

☞ The Golden Ratio in religions or mysticism.

☞ The FreeMasons and The Golden Ratio.

☞ Stargazing to find the Golden Ratio.

☞ Penrose tiles and the Golden Ratio.

There's lots on the Golden Ratio and Fibonacci on the internet... but be careful, a lot of supposed fact is actually myth!

To watch a very entertaining Stanford mathematician talk about the Golden Ratio see Keith Devlin exposes Fibonacci and the Golden Ratio

A couple of web sites...

These web sites are a good place to start... then try to find some of your own.

www.mathsisfun.com/numbers/golden-ratio.html

MARY HENRY, whose abstract art is a particular delight for lovers of geometry, has died aged 96.
An exhibition of her work can be seen at PDX Contemporary Art, 925 NW Flanders, Portland, OR 97209 until the end of May.

## New biggest prime found

The biggest prime number yet has been found with some 12,978,189 digits. It would fill nearly 20 paperbacks if printed out.

It's also the 45th known Mersenne prime, a rare sort of prime written as a power of 2 subtract 1: 243,112,609 − 1.

That's 2 multiplied by itself 43,112,609 times and then subtract 1.

A prime number can only be divided by the number 1 and itself — it has only two factors.

The discovery by the UCLA math department qualified for a \$100,000 award for the first prime of more than 10 million digits.

It was discovered using software from the Greater Internet Mersenne Prime Search — GIMPS — that allows anyone with a PC or laptop to help search for the next largest prime.

This new big prime was discovered in August 2008. Just two weeks later another — smaller — 46th Mersenne prime was discovered near Cologne, Germany: 2 37,156,667 − 1. It has a mere 11,185,272 digits.

Mersenne primes were first discovered by the French monk and mathematician Marin Mersenne more than 300 years ago.

Searching for primes was the sort of thing maths people did for fun, they still do. But now super-big primes are vital in internet and banking security as well as writing ultra-secret codes.

Mathematicians know there are an infinite number of primes. They think there an infinite number of Mersenne primes, but the conjecture has yet to be proved.