(Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in...

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(Greek γεωμετρία; geo = earth, metria = measure) developed to meet practical needs in surveying , construction , and astronomy

Transcript of (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in...

Page 1: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

• (Greek γεωμετρία; geo = earth, metria = measure)

• developed to meet practical needs in surveying, construction, and astronomy

Page 2: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

25,000 BC

Paleolithic PeriodCro-Magnon men made primitive geometricaldesigns

Page 3: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

2000-500 BC

Egyptians and Babylonians

could compute pythagoreantheorem & area but used“trial & error”; not logicallydeduced; Egyptians usedgeometry for taxing land afterthe Nile flooded each year

Page 4: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

800 BC

India

used geo. constructionsto solve linear/quadraticequations; est. pi to 5decimal places

Page 5: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

600 BC

Thales of Miletus

Greeks:

brought the science ofgeometry from Egyptto Greece. Thales is frequently credited with developing 5 theorems of elementary geometry.

Page 6: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

450 BC

Pythagorus

The 1st to logically deducegeometric facts from basicprinciples. Derived sum ofangles of triangles & thepythagorean theorem.

Page 7: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

400 BC

Hippocrates

Wrote the 1st

“Elements ofGeometry”. HippocraticOath

Page 8: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

300 BC

Plato

Emphasizedproofs & concisedefinitions. Platonicsolids

Page 9: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

300 BC

Euclid

Father of Geometry -collected theoremsfrom predecessors &wrote 13-book treatise.

Page 10: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

250 BC

Archimedes

The greatest of allGreek mathematicians-invented the screw, thepulley, & the lever.

Page 11: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

200 BC

Appollonius

Famous forwork in conics.

Page 12: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

150 BC

Hypsicles

described the 360Parts of a circle asdegrees.

Page 13: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

140 BC

Hipparchus

Famous for workin trigonometry.

Page 14: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

50 AD

Heron

Wrote“Metrica”(plane &3-D objects)

Page 15: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

100 AD

Ptolemy

Geometry ofplanetary motion

Page 16: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

120 AD

Chang Hong

Calculated pi to be3.1555

Page 17: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

Hypatia

400 AD

1st woman tosignificantly contribute tomathematics.

Page 18: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

Widmann

1489 AD

1st mathematicianTo use the notation+ and -.

Page 19: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

1600 AD

Coordinate Geometry:

Rene Descartes: Made one of the greatest advances in geometry by connecting algebra and geometry. A myth is that he was watching a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Maybe this has something to do with the fact that he stayed in bed everyday until 11:00 A.M. Fermat also discovered coordinate geometry, but it's Descartes' version that we use today.

Page 20: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

1706 AD

William Jones was the first

to use the π symbol to denote the

periphery (circumference) of a

circle with a diameter of 1.

Page 21: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

early 1800’s

Non-Euclidean Geometries

Since mathematicians couldn't prove the 5th postulate, they devised new geometries with "strange" notions of parallelism. (A geometry with no parallel lines?!?) Bolyai and Lobachevsky are credited with devising the first non-euclidean geometries.

Page 22: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.

late 1800’s – 1900

Differential geometry: combines geometry with the techniques of calculus to provide a method for studying geometry on curved surfaces.

Fractal geometry: geometric figures that model many natural structures like ferns or clouds. The invention of computers has greatly aided the study of fractals since many calculations are required.

Page 23: (Greek γεωμετρία; geo = earth, metria = measure)Greek developed to meet practical needs in surveying, construction, and astronomy surveyingconstructionastronomy.