ancient mathematics

MATHEMATICALINVENTIONS

One of the many great mathematical discoveries of Archimedes was the relationship between the surface area of a cylinder and a sphere. Archimedes discovered that a sphere that has the same diameter as the height and width of the cylinder is 2/3 of the surface area of the cylinder

Archimedes' Greatest Mathematics

Archimedes’ first war invention was a claw that was said to be able to lift ships out of the water and then smash them. From Pappus we have learned that in connection with his discovery of the solution to the problem of moving a given weight by a given force, that Archimedes upon applying the law of the lever is to have said, “Give me a place to stand on, and I can move the earth.”

Archimedes taking his bath on day, he noticed that that the level of the water in the tub rose as he got in, and he had the sudden inspiration that he could use this effect to determine the volume (and therefore the density) of the crown. In his excitement, he apparently rushed out of the bath and ran naked through the streets shouting, "Eureka! Eureka!" (“I found it! I found it!”). This gave rise to what has become known as Archimedes’ Principle: an object is immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

The circumference of a circle is the actual length around the circle which is equal to 360°. Pi (p) is the number needed to compute the circumference of the circle. p is equal to 3.14.Pi is greek and has been around for over 2000 years! In circles the AREA is equal to 3.14 (p) times the radius (r) to the power of 2. Thus the formula looks like:A= pr2.In circles the circumference is 3.14 (p) times the Diameter. Thus the formula looks like:2pr or pd.

Lines in Circles.AB = Diameter, OC = Radius,ED = Chord, FG = Tangent, EHD = Arc, ADB = Semicircle, OCB = Sector, COB = Central Angle.

Galileo’s Invention in Mathematics

Plate portraying soldiers using a compass to measure the barrel of a cannon. Jim Bennet, Stephen Johnston (edited by), The Geometry of War (1500-1750), Oxford, 1996, p. 15.Using instruments was indispensable in the military field, where the technology of firearms called for increasingly more precise mathematical knowledge.al

This 19th century model is based on a drawing made by Galileo's (1564-1642) friend and biographer Viviani (1622-1703) of a pendulum clock, which Galileo designed just before his death and which was partly constructed by his son Vincenzio in 1649. It represents the first known attempt to apply a pendulum to control the rate of a clock. He recognised the potential of using a pendulum to control a clock but died before his work could be completed.

Box for mathematical instruments (17th ca.), Florence, Istituto e Museo di Storia della Scienza .This box contains a set of mathematical instruments dating from the 17th century, coming from the Medicean collections. The interior, divided into nineteen compartments, now holds thirteen pieces, all made of brass: various instruments for drawing, a pair of knives and a proportional compass.

Mordente’s compass (1591), Florence, Istituto e Museo di Storia della Scienza. Invented by Fabrizio Mordente (1532 – c. 1608) to measure the smallest fraction of a degree, this particular proportional compass with eight points is distinguished by the presence of sliding cursors. Based on their positions, it was possible to establish the proportions between lines, geometric figures and solid bodies.

Geometric and military compass of Galileo Galilei (c. 1606), Florence, Istituto e Museo di Storia della ScienzaThe Istituto e Museo di Storia della Scienza of Florence possesses one of the very rare surviving examples of Galileo’s compass, probably the one donated by the Pisan scientist to Cosimo II along with a printed copy of the Operazioni del compasso geometrico et militare.

Leonardo Da Vinci Inventions in Mathematics

3-Dimensional figuresLeonardo da Vinci kept also busy with complex

3-dimesional geometric figures. Leonardo drew these in all their variants. In his period in Florence he was already introduced to the perspective geometry . The abstract perfection from these complex figures must have charmed and fascinated him.

The rhombicuboctahedron, as published in De divina proportione.

Mathematical Instrument Used In Ancient Period

Mathematicians

Tycho Instrument – Sextant

Old Computing Machines Made By Mathematics Logics

A calculating machine in the 17th century.

In 1888, William S. Burroughs patented his first calculator. Like the Comptometer, it was really an adder-subtracter, but it could multiply and divide via repeated additions and subtractions

1876 Centennial Expo Geo B Grants calculating machine.

In 1851, J. W. Nystroms calculating machine.

The Arithmetical machine (pictured) is one of the first mechanical calculating devices known to exist.

Islamic Inventions in Mathematics

Magnetic compass

A Geometrical Instrument used in measuring angles.

Earliest surviving Astrolabes…

Ancient Water Clock in Quanat of Gonabad, 500 years ago.

Islamic Symmetric design….

The World’s oldest known measuring device, The Lebombo Bone (35,000 BC) with 29 lines, Africa.

Ancient Magnetic Compass and Nowadays Magnetic Compass

Ancient Clocks

Water Clock Sun Dial

A Sun Dial, Dublin in 1742

Sand Clock