Answers to mathematical digest 128
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NEWTON, DESCARTES, EULER, GAUSS, PASCAL, PACIOLI, EUCLID, NEWTON, FERMAT, BABBAGE, ARCHIMEDE.

THE SQUARE OF THE HYPOTENUSE OF A RIGHT TRIANGLE IS EQUAL TO THE SUM OF THE OTHER TWO SIDES.

Evariste Galois
algebra sets

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J A C O B   B E R N O U L L I

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Jacob Bernoulli
The sphere has exactly 2/3 the volume of the cylinder.
Pythagoras. Pythagoras lived from around 569BC to 475BC. The first bound books appeared around 100BC.

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e= vertices   f = faces   k = edges
cube                          e = 8     f = 6   k =12         8 -12 + 6 = 2
tetrahedron               e = 4     f = 4   k = 6          4 - 6  + 4 = 2
triangular prism        e = 6     f = 5   k = 9          6 - 9  + 5 = 2
hexagonal prism      e = 12   f = 8   k = 18      12 - 18  + 8 = 2
a2 + b2 = c2                       to do with right angled triangles
(a+b)2 = a2 + 2ab + b2    an algebraic equation formula
H3PO4                               a formula for a chemical
F = mxa                              a formula for motion

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They are all impossible to make!

For the drawing of the logarithmic spiral see "unusual lessons - the golden ratio".

Jacobs staff was a wooden cross used by sailors to find the elevation angle of the sun above the horizon,  at noontime.  From this sailors could calculate their lattitude. The problem was it could not be used on cloudy days and on sunny days navigators could go blind by looking directly into the sun.
It works by similar triangles.

The shape is the Mobius strip. It is a one sided piece of paper!

Fermat's formula   xn + yn = zn is not true if n >2.

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The movie was Merry Andrew.
-and it is all about "the square of the hypotenuse of a right angled triangle is equal to...   see page 2 of this digest!

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In order, the number line should show
Galileo, Descartes, Fermat, Pascal, Newton, Seki, Leibnitz, Monge, Gauss, Cauchy, Galois, Kovalevskaya, Curie, Rutherford, Einstein, Ramanujan.

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Fermat,   Jacob Bernoulli,  Euler,  Newton

It is a rectangle with dimensions 22 by 21.

Newton and Leibnitz          possible but probably not - they corresponded - but not friendly!
Fermat's pen pals              Mersenne, Pascal, Descartes, ...
Pascal and Descartes       Descartes visited Pascal in Rouen in September 1647.
                                              Pascal was 24 and Descartes 51.
Newton and Galileo            Galileo died in Jan 1642 and Newton was born in Dec 1642 (or Jan 1643).

Ramunjan and Rutherford.  Possible. Ramunjan lived in Trinity College Cambridge from 1914 to Feb1919.                    Rutherford lived at Trinity College 20 years before this time and had become a Professor in Manchester. He became Director of the Cavendish Laboratory at Cambridge later in 1919. It is possible he may have visited Trinity College whilst Ramanujan was there and they might have met. There is no record to show that they did.

Einstein and Curie              Yes they almost certainly did. There are photos of them together -
                                              see Maths Digest number 123
Who lived the longest?       Without doubt Sir Isaac Newton  84 years
Most were alive between 1646 and 1650.

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Isaac Newton was born on Christmas day 1642 according to the Julian calendar in use in Britain at that time.
In Europe the calendar that was being used was the more modern Gregorian calendar. Under the Gregorian calendar 25th Dec 1642 becomes 4 Jan 1643. see Maths Digest number 127 for more details.


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