1. Archimedes Of Syracuse
2. Archimedes Spiral
3. List Of Archimedes Inventions
4. Archimedes Ships
5. Archimedes Screw
6. Archimede Watches

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Archimedes was an ancient Greek mathematician and inventor. He made mathematical discoveries as he solved everyday problems. He invented machines to move heavy objects, carry water, and fight battles. Archimedes recorded his discoveries so that others could learn from them. Archimedes, (born c. 287 bce, Syracuse, Sicily Italy—died 212/211 bce, Syracuse), the most famous mathematician and inventor in ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. Archimedes' Principle. If the weight of the water displaced is less than the weight of the object, the object will sink; Otherwise the object will float, with the weight of the water displaced equal to the weight of the object. 212 BCE) was a truly great inventor, mathematician and philosopher, writing many insightful and extensive treatises on geometry and applied mathematics.

Archimedes is one of history's great thinkers. He was astute in philosophy as well as in the arts, active in mathematics and physics, and was recognized as one of the greatest engineers of his time. His legacy lives on in the modern era through historical accountsof his countless inventions and discoveries from 2000 years ago.

Let's take a look at 7 inventions that Archimedes was responsible for.

Archimedes’ screw

One major concern of farmers in pre-industrial society was the need to irrigate their land, a considerable issue in the time before sophisticated pumping systems. Different cultures had different ways of dealing with this. One solution, whose introduction into ancient Greece has been credited to Archimedes, was the water screw or screw pump, which is more commonly known today as the Archimedes Screw.

This screw-shaped device was rotated by a windmill or through manual labor. As the entire unit rotated, water was lifted inside the spiral tube to a higher elevation.

The design of this device was so useful that it has even carried over into other industries, where it has been used to move light materials like grain in and out of farming silos.

Archimedes' principle

Archimedes is credited as the person who discovered the principle of buoyancy, which is also known as Archimedes' Principle. This states that a body completely or partially submerged in a fluid at rest is acted upon by an upward, or buoyant, force, and that the magnitude of this force is equal to the weight of the fluid displaced by the body.

The story goes that Archimedes discovered this principle after being tasked by the king to figure out whether a crown made for him was pure gold, or whether it contained other metals. Archimedes realized that if he took a lump of gold weighing the same as the gold crown, the two objects should displace the same amount of water, regardless of shape.

If the goldsmith who made the crown replaced any of the gold with a cheaper metal, then the crown would displaced more water.

According to the story, Archimedes used this idea to prove that the goldsmith had cheated the king out of a rightful amount of gold in the crown.

Stories differ on how Archimedes was actually able to discover that the crown wasn't pure gold.

The Iron Claw

Archimedes is particularly famous for designing war machines for his home state of Syracuse, during the Punic Wars. One famous device was called the Iron Claw, which is also known as the Claw of Archimedes.

This machine was thought to have been installed on the seaward-facing walls of the city of Syracuse, to protect the city against amphibious assault. The device is only known about only through snippets of historical accounts, but it was believed to have been some type of crane, with a grappling hook on one end, which was able to lift attacking ships partly out of the water, and then either cause the ship to capsize or suddenly drop it. It may also have been dropped onto enemy ships, to cause them to swing around and destroy themselves.

The odometer

Archimedes has also been credited as coming up with the first idea for an odometer, or at least a mechanical method of keeping track of distance traveled. Drivers 3dsp port devices.

The Roman engineer Marcus Vitruvius Pollio (80/70 BC-15 BC), wrote an account of this idea, which he credited to Archimedes. The odometer operated on the idea that every time a wheel goes around, it travels its own circumference. The odometer may have used a large wheel of a known circumference, along with a series of gears.

The theory is that a gear on the drive shaft had only one tooth and a gear holding a box of pebbles had additional teeth. Every time the chariot wheel goes completely around, the pebble-gear moves one notch. After the wheel had gone enough revolutions to equal one mile, the pebble-gear would have moved so that a hole leading from the pebble box lined up with a hole underneath the gear and a pebble dropped into a bucket. Counting the pebbles could tell you how many miles had been travelled. Each dropped marble represents one mile traveled.

The pulley system

Archimedes didn't invent the pulley, but he did develop different systems of compound pulleys, improving on the existing technology that was around at his time. He clearly demonstrated that a wheel supported by a rope could be used as a method of transferring energy, providing the operator with a mechanical advantage in the process.

Archimedes developed an efficient a block and tackle system, allowing sailors to use leverage to lift heavy objects.

The law of the lever

Archimedes is also credited with finding new uses for the lever. The great inventor supposedly once said, 'Give me a place to stand on, and a lever long enough, and I will move the earth.' To which he was challenged to prove it.

In one story, he was tasked with launching Syracuse's largest ship. Archimedes is said to have accepted the task and utlized a massive lever mechanism along with a series of pulleys to launch the newly-constructed ship.

Although, Archimedes was not the first to conceive of a lever mechanism, he accurately described the underlying physics and explained the ratios of force, load, and how the fulcrum point interacted with a lever's capability.

Geometry of shapes

The Roman historian Plutarch wrote that Archimedes did not hold his own mechanical inventions in high regard. Rather, he was much prouder of his proofs and theorums in the realm of physics and mathematics. The great engineer is credited with proving that the area of a circle is equal to π multiplied by the square of the radius of the circle. He also proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a corresponding inscribed triangle.

As you can probably tell from this brief list though, the inventor had a significant hand in the elucidation of early physics, mathematics, mechanical design, and even art. He was arguably the greatest polymath to ever live and rightfully deserves his place in the history books.

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Archimedes of Syracuse

Born: 287 BC in Syracuse, Sicily
Died: 212 BC in Syracuse, Sicily

Archimedes, the greatest mathematician of antiquity, made his greatest contributions in geometry. His methods anticipated the integral calculus 2,000 years before Newton and Leibniz.

He was the son of the astronomer Phidias and was close to King Hieron and his son Gelon, for whom he served for many years.

He was an accomplished engineer but loved pure mathematics.

Stories from Plutarch, Livy, and others describe machines invented by Archimedes for the defense of Syracuse. These include the catapult, the compound pulley and a burning-mirror.

Among Archimedes most famous works is Measurement of the Circle, in which he determined the exact value of to be between the values and . This he obtained by circumscribing and inscribing a circle with regular polygons having 96 sides. However, he required the proof of two fundamental relations about the perimeters and areas of inscribed and circumscribed regular polygons.

The computation. With respect to a circle of radius r, let

Further, let denote the regular inscribed polygons,similarly, for the circumscribed polygons.The following formulae give the relations between the perimeters and areas of these polygons.

Archimedes Of Syracuse

Using n-gons up to 96 sides he derives

Archimedes Spiral

Archimedes -- Books Extant

On the Sphere and Cylinder

Measurement of the Circle

On Conoids and Spheroids

On Spirals

On Plane Equilibria, Two Books

The Sand-Reckoner

Quadrature of a Parabola

On Floating Bodies: two Books

Stomachion, fragments only

The Method

Archimedes proved, among many other geometrical results, that the volume of a sphere is two-thirds the volume of a circumscribed cylinder.

This he considered his most significant accomplishments, requesting that a representation of a cylinder circumscribing a sphere be inscribed on his tomb.

His fascination with geometry is beautifully described by Plutarch. Often times Archimedes' servants got him against his will to the baths, to wash and anoint him, and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savors, with his figures he drew lines upon his naked body, so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry.

Archimedes literally invented the whole study of hydrostatics. In one particular result he was able to compute the maximum angle that a (paraboloid) ship could list before it capsized -- and he did it without calculus!

The case of the fraudulent gold crown. King Hiero II commissioned the manufacture of a gold crown. Suspecting the goldsmith may have substituted silver for gold, he asked Archimedes to determine its authenticity. He was not allowed to disturb the crown in any way.What follows is a quote from Vitruvius (first cent BC):

The solution which occurred when he stepped into his bath and caused it to overflow was to put a weight of gold equal to the crown and know to be pure, into a bowl which was filled with water to the brim. Then the gold would be removed and the king's crown put in, in its place. An alloy of lighter silver would increase the bulk of the crown and cause the bowl to overflow.

There are some technical exceptions to this method.A better solution applies Archimedes' Law of Buoyancy and his Law of the Lever:

List Of Archimedes Inventions

Suspend the wreath from one end of a scale and balance it with an equal mass of gold suspended from the other end. Then immerse the suspended wreath and gold into a container of water. If the scale remains in balance then the wreath and the gold have the same volume, and so the wreath has the same density as pure gold. But if the scale tilts in the direction of the gold, then the wreath has a greater volume than the gold.

He explores very large numbers in the Sand Reckoner by determining the number of grains of sand required to fill the universe of Aristarchus. To do this he needs new numbers and notations for magnitude. He constructed numbers up to .

Archimedes discovered fundamental theorems concerning the center of gravity of plane figures and solids. His most famous theorem gives the weight of a body immersed in a liquid, called Archimedes' principal.

In The Method Archimedes reveals how he discovered some of his theorems. The method is basically a ``geometric method of the lever.' He balances lines as one might balance weights. This work was found relatively recently, having being rediscovered only in 1906.

Archimedes' mechanical skill together with his theoretical knowledge enabled him to construct many ingenious machines.

Archimedes spent some time in Egypt, where he invented a device now known as Archimedes' screw. This is a pump, still used in many parts of the world.

Quadrature of a Parabola. Archimedes proved, with the Method of Exhaustion, that

and gave two proofs.

The Spiral. Archimedes squared the circle using thespiral.

He does this by proving that, in length, . Note, PQ is tangent to the spiral at P and is a right angle.

He also determined the area of one revolution ( ) of to by

That is, the area enclosed by the spiral arc of one revolution is one third of the area of the circle with center at the origin and of radius at the terminus of the spiral arc.

He also showed how to trisect the angles using the spiral.Simply construct circles of radii with constant successive differences. These circles will cut the spiral at equal angles. To trisect a particular angle, simply trisect a radial line segment corresponding to the values of the radii at the intersection of the spiral and lines that make the angle (with vertex at the origin). Construct the circles at the trisection points, with centers at the origin.

Archimedes Ships

Archimedes was killed during the capture of Syracuse by the Romans in the Second Punic War. Plutarch recounts this story of his killing: As fate would have it, Archimedes was intent on working out some problem by a diagram, and having fixed both his mind and eyes upon the subject of his speculation, he did not notice the entry of the Romans nor that the city was taken. In this transport of study a soldier unexpectedly came up to him and commanded that he accompany him. When he declined to do this before he had finished his problem, the enraged soldier drew his sword and ran him through.

Archimedes Screw

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Archimede Watches

Don Allen
Wed Feb 19 08:06:42 CST 1997