The Second Book of General Ignorance by John Lloyd, John Mitchinson Page A
Authors: John Lloyd, John Mitchinson
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his sword more effectively, but it would also give a right-handed attacker the same advantage. So, a staircase that twisted the other way would only be useful when defending against another Kerr (not impossible given their bloodthirsty reputation).
The Chateau de Chambord in the Loire Valley has a double-helix staircase: two staircases which wind around each other so that people going up don’t bump into people coming down – and the cliff-top fortifications at Dover have a triple -helix staircase (known as the ‘Grand Shaft’) designed to get three columns of troops down to harbour level simultaneously.
The most famous of all double helixes is the molecule called deoxyribonucleic acid, better known as DNA. Francis Crick and James Watson first described its structure in 1953, although they were inspired by an X-ray photograph of DNA taken by Rosalind Franklin (1920–58), who almost beat them to it.
If you unravelled all the DNA strands in your body they’d stretch for 1,000 billion kilometres (620 billion miles), which is nearly 7,000 times further than the distance to the sun, and further away in the other direction than the edge of the Solar System.
To put that in perspective, to count to 620 billion you would have to have started 20,000 years ago, in the middle of the last ice age.
What’s so great about the golden ratio?
Every Dan Brown fan has heard of this mysterious figure that crops up everywhere – in the human body, in ancient architecture, in the natural world – and whose appeal nobody can explain. The truth is that it doesn’t appear in most of the places it’s supposed to, and many of the claims about it are false.
The golden ratio (also known as ‘the golden mean’ or the ‘divine proportion’) is a way of relating any two quantities – such as the height (a) of a building to the length (b) – in the following simple way.
In the nineteenth century, this ratio was given the name phi – φ – after the great Greek sculptor Phidias (490–430 BC ), who supposedly used it in the proportions of his human figures. The reason that such a simple formula produces such a complicated, unharmonious looking number is that phi (φ), like pi (π), cannot be written as a neat fraction, or ‘ ratio ’, so it is called an ir ratio nal number. Irrational numbers can only be expressed as an infinite string of decimal places that never repeat themselves. A prettier way of expressing phi in maths is: (√ 5+1) divided by 2.
A ‘golden spiral’ is one that gets further from its central point by a factor of φ for every quarter turn it makes. A frequently quoted example of this is the beautiful shell of Nautilus pompilius , a member of the octopus family. But in fact this is a ‘logarithmic spiral’, not a golden one. In 1999 the American mathematician Clement Falbo measured several hundred shells and showed quite clearly that the average ratio was 1 to 1.33: a long way from 1.618. (If you did want to use a shell to demonstrate the golden mean, the abalone would do well, but they’re not nearly as photogenic as the nautilus.)
The Greeks knew about the golden ratio, and the Parthenon is the usual example given of its use in architecture. But any diagrams showing how its side or front elevations demonstrate a ‘golden rectangle’ always either include some empty air at the top or leave out some steps at the bottom.
The golden ratio was forgotten for hundreds of years after the fall of Rome, until Luca Pacioli (1446–1517), a Franciscan monk and Leonardo da Vinci’s tutor, wrote about it in De Divina Proportione (1509). Leonardo did the illustrations for the book but, despite what it says in The Da Vinci Code , he did not use the golden ratio to compose either the Mona Lisa or his famous 1487 drawing of a man in a circle with his limbs extended.
The latter is called Vitruvian Man after the Roman architect Vitruvius, who lived in the first century BC and is sometimes called ‘the world’s
The Chateau de Chambord in the Loire Valley has a double-helix staircase: two staircases which wind around each other so that people going up don’t bump into people coming down – and the cliff-top fortifications at Dover have a triple -helix staircase (known as the ‘Grand Shaft’) designed to get three columns of troops down to harbour level simultaneously.
The most famous of all double helixes is the molecule called deoxyribonucleic acid, better known as DNA. Francis Crick and James Watson first described its structure in 1953, although they were inspired by an X-ray photograph of DNA taken by Rosalind Franklin (1920–58), who almost beat them to it.
If you unravelled all the DNA strands in your body they’d stretch for 1,000 billion kilometres (620 billion miles), which is nearly 7,000 times further than the distance to the sun, and further away in the other direction than the edge of the Solar System.
To put that in perspective, to count to 620 billion you would have to have started 20,000 years ago, in the middle of the last ice age.
What’s so great about the golden ratio?
Every Dan Brown fan has heard of this mysterious figure that crops up everywhere – in the human body, in ancient architecture, in the natural world – and whose appeal nobody can explain. The truth is that it doesn’t appear in most of the places it’s supposed to, and many of the claims about it are false.
The golden ratio (also known as ‘the golden mean’ or the ‘divine proportion’) is a way of relating any two quantities – such as the height (a) of a building to the length (b) – in the following simple way.
In the nineteenth century, this ratio was given the name phi – φ – after the great Greek sculptor Phidias (490–430 BC ), who supposedly used it in the proportions of his human figures. The reason that such a simple formula produces such a complicated, unharmonious looking number is that phi (φ), like pi (π), cannot be written as a neat fraction, or ‘ ratio ’, so it is called an ir ratio nal number. Irrational numbers can only be expressed as an infinite string of decimal places that never repeat themselves. A prettier way of expressing phi in maths is: (√ 5+1) divided by 2.
A ‘golden spiral’ is one that gets further from its central point by a factor of φ for every quarter turn it makes. A frequently quoted example of this is the beautiful shell of Nautilus pompilius , a member of the octopus family. But in fact this is a ‘logarithmic spiral’, not a golden one. In 1999 the American mathematician Clement Falbo measured several hundred shells and showed quite clearly that the average ratio was 1 to 1.33: a long way from 1.618. (If you did want to use a shell to demonstrate the golden mean, the abalone would do well, but they’re not nearly as photogenic as the nautilus.)
The Greeks knew about the golden ratio, and the Parthenon is the usual example given of its use in architecture. But any diagrams showing how its side or front elevations demonstrate a ‘golden rectangle’ always either include some empty air at the top or leave out some steps at the bottom.
The golden ratio was forgotten for hundreds of years after the fall of Rome, until Luca Pacioli (1446–1517), a Franciscan monk and Leonardo da Vinci’s tutor, wrote about it in De Divina Proportione (1509). Leonardo did the illustrations for the book but, despite what it says in The Da Vinci Code , he did not use the golden ratio to compose either the Mona Lisa or his famous 1487 drawing of a man in a circle with his limbs extended.
The latter is called Vitruvian Man after the Roman architect Vitruvius, who lived in the first century BC and is sometimes called ‘the world’s
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