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3. Everything / Maths, Science & Technology / Mathematics

The Helix

A helix is a type of three-dimensional spiral: it is the shape of the handrail of a spiral staircase, of the thread of a bolt, or of the twisty bit of your average corkscrew. Hopefully these examples will make it clear to you what we're talking about, because the helix is notoriously difficult to describe clearly in abstract terms. You can get great amusement by asking your friend to describe the shape of a spiral staircase without using his or her hands.

The plural of the word helix is helixes or helices depending on how pedantic you are.

Uses of the Helix

Helixes are used in many applications in modern life.

Going up and down

The spiral staircase is probably the example of the helix that most of us are familiar with. The usual form has a central pillar with the steps all joined to the pillar. It is the outer edge of the staircase that is in fact a helix. Spiral staircases are useful for fitting a stair into a very small space, but are difficult to climb, so are recommended only for infrequent use.

In medieval times, it was normal to fit a spiral staircase into a cylindrical shaft in the building, so that the person climbing would have the central pillar on one side and a wall on the other side. There was normally no handrail on the wall side. People using the stair would hold on to the central pillar. In medieval castles, it was normal to have the stair curving to right as you ascended, so that the central pillar was on the right-hand side. This is said to be so that an attacker climbing the stairs would not be able to hold his sword in his right hand and hold on to the pillar at the same time (most attackers would be right-handed). On the other hand, defenders coming down the stair would have the pillar on their left, allowing them to hold on while wielding a sword in their right hand.

Monasteries, in an attempt to show that they were not interested in defence, traditionally had their spiral staircases curving in the opposite direction so that the central pillar was on the left for the climber.

The helter skelter is in effect the opposite of a spiral staircase - a way of descending quickly in a helical path. It is a slide that has been twisted into a helix. These are sometimes found in funfairs. A mat may be provided to make the passage smoother and faster.

Springs

A spring is a device for using the elasticity of metal. The helical spring is the most common sort. A thin piece of metal is coiled into a helix, and hooks are added at each end. Springs can be used for a number of different purposes:

• Storing energy: the up-and-over garage door stretches two giant springs when the door is closing. The weight of the door stores energy in the springs. The energy is retrieved when the door is opened; the springs assist the door in opening against gravity.

• Springs obey Hooke's Law - they stretch in proportion to the applied force. This means they can be used for measuring a force, usually the weight of something. The simplest example of this is the weighing device used by anglers to measure the one that didn't get away - basically a spring attached to a pointer. More elaborate arrangements of springs and levers are used in the bathroom scales, used the world over by dieters.

• Making something soft - springs in a bed make it soft as it moves under you.

The Bolt

The bolt is a cylinder of metal with a helical thread and a head at one end which can be gripped to allow the bolt to turn. Bolts are used for attaching things to other things, and can be used with a nut, or with a threaded hole in one of the two things to be attached. A bolt amplifies the force applied to the head, and attenuates the force applied to the threads, meaning that it is easy to tighten, but will not work loose by itself.

A puzzle involving two bolts is known as 'The Twiddled Bolts'. Take two bolts and hold one in each hand by the head, so that they face each other. Mesh the threads on the two bolts so that one is lying alongside the other and touching it along its length. Now 'twiddle' the bolts so that each goes in a circle around the other, with the threads staying intermeshed. Do this in such a direction that the top bolt is moving away from you. The question is, will the bolts be pulled towards each other by the thread, pushed apart or stay the same?1

Corkscrew

A corkscrew is an example of helix. The simplest corkscrew is just a helix attached to a handle, but this requires a lot of strength to pull the cork, so most corkscrews have an arrangement of levers to make it easier to pull the cork.

Worm Gear

The worm gear uses a helical gear in combination with a normal circular gear to provide a very larger gear ratio. Each complete turn of the helical gear turns the circular gear by only one tooth.

Archimedes Screw

The great Greek mathematician is said to have invented this device which has probably done more for the history of agriculture than any device other than the plough. A helical tube lying at an angle of 45° will raise water in its coils. All you need is something to turn the screw - this can be done by people power, by wind or even by the power of a flowing stream. Such Archimedes screws are used in their millions for irrigation in Egypt and other well-watered but dry countries.

Helixes in Nature

• The tendrils of some climbing plants, in particular bindweed and honeysuckle, spiral around other plants to grip onto them.

• The buds of most woody plants spiral around a twig in a helical pattern.

• The alpha helix is a common structure in proteins within all life. In it, amino acids are linked together into a helix.

Mathematics

The helix is a mathematical curve. A vertical axis helix, such as a spiral staircase, can be defined by two equations in x, y and z:

x = r.cos(f.z), y = r.sin(f.z)

Here r determines the radius of the helix and f determines the steepness with which the helix ascends.

Pitch

Rather than talking about angles, engineers and technologists talk about the pitch of the helix - the number of turns per inch, metre or any other suitable measure.

Pedantic Mathematicians

Mathematicians have been known to insist that a helix is not a spiral and that the word spiral should be reserved for the flat type of spiral which circles outwards from a point. Let them; we'll continue to talk about helixes spiralling, as it is commonly understood.

The Double Helix

Two helixes can share the same axis and can nest together without touching each other. Each one sits in the space left by the other. A wonderful example of this can be found in the Vatican Museum, in Rome. There is a tall cylindrical hall, with two spiral staircases. Unlike the normal type with a central supporting pillar, these are attached only to the outer wall. The two staircases form a double helix, and each one ascends without touching the other. To accentuate this, one is reserved for people going up and the other for people coming down. You can see the people on the other side of the hall going in the opposite direction, but you never meet them.

DNA

Double helixes also occur in every cell in your body. The DNA which carries the instructions for building the cell is in the form of a double helix. The two strands which form the double helix are made up of alternating sugar and phosphate units. There are horizontal 'rungs' joining the two strands together and it is these rungs which carry the information of the DNA.

The Triple Helix

Just as two helixes can fit snugly together, so too can three, four or any number you like. Such high-order helixes are rarely found in nature, but there are a few examples of the triple helix: strands of keratin, one of the main components of hair, sometimes form into a triple helix, as do the proteins that make up collagen, a component of skin, cartilage and bone.

Other meanings for the word Helix

And finally, the word helix is also used for a number of other things:

• A brand of ruler in the UK.
• The rim of the external ear.
• A genus of gastropod which includes the common garden snail.
• An Australian literary journal in the period 1978 - 1986.
• The spiral or 'volute' in the capital of a Greek column.
• The curly bit at the end of a banister rail over the newel post.
• 'The Helix' is a concert hall in Dublin, Ireland.
• 'The Helix Nebula' is a planetary nebula in Aquarius.

1 The bolts will in fact stay the same distance apart.

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Entry Data
Entry ID: A22691171 (Edited)

Written and Researched by:
U151503 - Gnomon - Future Guide Editor - towels at the ready

Edited by:
Skankyrich

Date: 22   May   2007

 Referenced Guide Entries Greece How Proteins are Made Water Swords How to Lose and Control Weight Dublin, Ireland Gravity Great Castles An Introduction to Coarse Fishing Australia Constellations: Aquarius 'the Water Carrier'

 Related BBC Pages BBC News: 50 Years of DNA BBC Science and Nature

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Most of the content on h2g2 is created by h2g2's Researchers, who are members of the public. The views expressed are theirs and unless specifically stated are not those of the BBC. The BBC is not responsible for the content of any external sites referenced. In the event that you consider anything on this page to be in breach of the site's House Rules, please click here. For any other comments, please start a Conversation above.