Pythagoras and Geometry

Book Title : Geometry Mathsfill

Author : C.J. Davis

Level : GCSE

ISBN 9780956014672

GCSE MathsWorkbook

Applicationsof Geometry

History

of Geometry

Discoveries of famous mathematiciansRead about :

Euclid ( 365 – 265 BC ) Democritus ( 460 BC – 370 BC )

Some of the major contributors in the development of geometry.

Archimedes c. 290 BC

also :

Pythagoras c. 570 BC

exactly two-thirds that of the cylinder surrounding it.

the volume and surface area of a sphere is

proved that . . .

Archimedes

Archimedes was the first person

to give the exact expression for

the volume of a sphere . . .

43 r

3 V =

The medal carries a portrait of

Archimedes. The inscription around the

medal is a quote in Latin attributed to Archimedes :

“Rise above oneself and grasp the world.”

The Field’s medal is awarded

to mathematicians of

outstanding achievement.

The Field’s Medal

Volume of pyramid, V = x area of base x height

. . . worked on the general formula for the volume of a pyramid :

Democritus

For a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

is best known for his Pythagorean theorem which states :

Pythagoras

Old Babylonian "hand tablet" illustrating Pythagoras' Theorem and an approximation of the square root of two.

The Babylonians understood this rule

1 000 years earlier, but Pythagoras proved it.

. . . created the earliest systems

. of weights and measures ?

WHO . . . ?

. . . devised the Metric system ?

The Metric system was created by the French Academy of Science in 1793.

A team of mathematicians and scientists were involved in its creation.

Antoine Lavoisier (1743 -1794)

This included the mathematician Joseph Lagrange and the chemist Antoine Lavoisier.

GCSE MathsWorkbook

Applicationsof Geometry

History

of Geometry

WHAT . . . ?

. . . is the numerical value . of pi ?

HOW . . . ?

is trigonometry used to

calculate the height

of a tree ?

WHAT . . . ?. . . is the Cornrow Curves Software ?

. . . are the four geometric concepts used to create cornrow hairstyles ?

www.rpi.edu/~eglash/eglash.htm

The Cornrow Curves software was created by Prof. Ron

Eglash and allows you use geometrical knowledge from

cornrow hairstyles to create your own simulated cornrow

designs on the computer.

www.rpi.edu/~eglash/eglash.htm

What are Fractals ?

Each leaf of this fern is in fact a smaller version of the entire fern. The whole fern is simply made up of reduced versions of itself. 

Fractals are images that exhibit something called self-similarity. 

e.g. something that is made up

of a reduced version of itself.

. . . is the link between

fractals, African art,

architecture and designs ?

WHAT . . . ?

The brachistochrone curve is an inverted cycloid.

The cycloid occurs as the curve generated by a point on a rolling circle.

HOW . . . ?

. . . is a cycloid generated ?

Is the shortest path always the quickest ?

WHICH . . . ?

Set up a straight line path and a brachistochrone and see !

. . . path is the quickest route to the bottom ?

  Linear Descent vs. the Brachistochrone

When two balls are dropped from the top of the straight ramp and the

the bottom first, even though the path it travels is longer.

brachistochrone

top of the brachistochrone, the ball on the brachistochrone reaches

GCSE MathsWorkbook

Applicationsof Geometry

History

of Geometry

- Time saving, write-on format.

- Clearly structured, easy to follow layout.

What are students saying about Geometry Mathsfill ?

A skateboard ramp has a height

of 1.05 m and a base of 2.24 m.

Calculate the length of the ramp,

2.24 m

1.05 m

m

…………………………………………….………..…..

……………………………………….… ……………m

…………………………………………….………..…..

…………………………………………….……………………...…..

………………………………………………….… ………….……km

…………………………………………….………………….…..…..

From take-off an aeroplane climbs at an angle12.

of 18. When the aeroplane has flown 15 km,

what vertical height has it reached ?

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ISBN 9780956014672

Geometry Mathsfill

(A5) Notepad format

Author: C.J. Davis

Publisher : Bookfill

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(A5) Notepad format

Algebra Mathsfill

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