des blast from the past

8/4/2019 des Blast From the Past

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http://upload.wikimedia.org/wikipedia/commons/e/e7/Domenico-Fetti_Archimedes_1620.jpg


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Syracuse

(then part of Greece)287-212 BC


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Discovered how to calculate the volumeof a sphere , and even wanted thisdiagram on his tombstone. He made somuch progress in this area that nothing

could be added for 18 centuries.

EUREKA (I have found it!) Bouyancy

Developed Exponential system ofwriting large numbers

Discovered the Law of the Lever

x2


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Italian postage stamp honoringArchimedes May 2, 1983Scott Catalogue Number 1559

This statue in the NationalMuseum in Naples, Italy, waswidely claimed to be Archimedes.

It is actually a bust of ArchidamosIII, a third century BC king ofSparta

Archimedes iscommemorated on aGreek postage stampfrom 1983.

The Fields Medal carries a portrait of Archimedes.
http://en.wikipedia.org/wiki/Fields_Medalhttp://en.wikipedia.org/wiki/Fields_Medalhttp://upload.wikimedia.org/wikipedia/commons/4/45/FieldsMedalFrontArchimedes.jpghttp://en.wikipedia.org/wiki/Image:Archimedes_greece_1983.png


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Archimedesdesigned many

tools for defendingSyracuse from

invasion. This is amodel of how one

of Archimedeswar gadgets may

have worked.
http://www.mcs.drexel.edu/~crorres/Archimedes/Claw/harris/anim-b.mov


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A detail of a wall painting in the Stanzino delleMatematiche in the Galleria degli Uffizi in Florence,Italy. Painted by Giulio Parigi (1571-1635) in the

years 1599-1600.


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Burning MirrorArchimedes used

mirrors to reflect andintensify the sun,

causing the ships tocatch on fire.
http://en.wikipedia.org/wiki/Image:Archimedes_Heat_Ray_conceptual_diagram.svg


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Wall painting from the Stanzino delle Matematichein the Galleria degli Uffizi (Florence, Italy). Paintedby Giulio Parigi (1571-1635) in the years 1599-1600.


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The death of Archimedes depicted on aRoman floor mosaic


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The Pythagoreans' believed All is Number,meaning that everything in the universe dependedon numbers. They were also the first to teach that

the Earth is a Sphere revolving around the sun.

Pythagoras is

often consideredthe first truemathematician.


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Pythagoras was born on Samos a Greek island off the coast of Asia Minor. Hewas born to Pythais (mom) and

Mnesarchus (dad).As a young man, he left his native city forSouthern Italy, to escape the tyrannicalgovernment. Pythagoras then headed toMemphis in Egypt to study with the priests

there who were renowned for their wisdom. Itmay have been in Egypt where he learnedsome geometric principles which eventuallyinspired his formulation of the theorem thatis now called by his name.

Towards the end of his life he fled to Metapontum becauseof a plot against him and his followers by a noble of Crotonnamed Cylon. He died in Metapontum around 90 years old

from unknown causes.

Life


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Many of Pythagorasbeliefs reflect those ofthe Egyptians. The

Egyptian priests werevery secretive. The

refusal to eat beans orwear animal skins andstriving for purity werealso characteristics of

the Egyptians.


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a 2 + b 2 = c 2


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Proof of Pythagorean theorem by rearrangement of 4identical right triangles. Since the total area and the areas ofthe triangles are all constant, the total black area is constant.But this can be divided into squares delineated by thetriangle sides a, b, c , demonstrating that a 2 + b 2 = c 2 .
http://upload.wikimedia.org/wikipedia/en/f/f7/Pythag.gif


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The sum of the angles of a triangle is equal to tworight angles or 180 degrees

The five regular solids

Venus as an evening star was the same planetas Venus as a morning star.

The abstract quantity ofnumbers. There is a big stepfrom 2 ships + 2 ships = 4ships, to the abstract result 2+ 2 = 4


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Regular Solids

Measure the net of this Tetrahedron andfind the surface area


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One of the Pythagoreans most important discoverieswas that the diagonal of the square is longer than itssides. This showed that irrational numbers existed

(decimal numbers that never end).

a

b

c a < cb < c
http://upload.wikimedia.org/wikipedia/commons/a/a6/Square_root_of_2_triangle.svg


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Pythagoras 569 B.C. 475 B.C.

Greece First pure mathematician 5 beliefs Secret society Pythagorean theorem


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Aristotle 384 B.C. 322 B.C.

Greece Philosopher Studied mathematics in

relation to science


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Al-Khwarizmi 780 A.D.-850 A.D.

Baghdad (in Iraq) 1st book on Algebra Algebra Natural Number Equation


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Leonardo da Vinci 1452 A.D. - 1519 A.D.

Italy Geometry with

mechanical methods

Painter Architect Mechanic


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Galileo Galilei 1564 A.D. 1642

A.D. Italy Teacher

Astrology Mathematician


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De Lhopital 1661 A.D. 1704 A.D.

France Differential Calculus LHopitals Rule


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Leonhard Euler 1707 A.D. 1783 A.D.

Switzerland Mechanica (book on

mathematical analysis)

Calculus of variations Analytic Geometry Trigonometry

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