The square root of 2, written 2 , is the positive solution of the
equation x 2 2.
It is an irrational number, that is to say a number that can’t be
a
written in the form , where a and b are both integers, with b≠
b
Its numerical value truncated to 3 decimal places is:1.414.
99
The quick approximation
for 2 is most frequently used
70
1
because it differs from the correct value by less than
.
10,000
Geometrically 2 is the length of a diagonal across a square with
sides of one unit of length; this follows from Pythagoras’
theorem.
2 is the aspect ratio of paper sizes under international standards
such A4, A3, etc. This ratio guarantees that cutting in half a sheet
by a line parallel to its short side results in two sheets having the
same ratio.
2
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The golden number, often designated by the Greek letter , is the
positive solution of the equation x 2 x 1.
It is an irrational number, that is to say a number that can’t be
a
written in the form , where a and b are both integers, with b≠
b
Its numerical value truncated to 3 decimal places is: 1.618.
The golden number is used to divide an object into 2 parts so that
the ratio of the larger to the smaller part is the same as the ratio of
the whole object to the larger part.
A golden rectangle, whose sides are in the golden ratio, has
throughout history been considered to have a particularly pleasant
shape.
Besides the Greeks used this number in the construction of the
Parthenon, and Renaissance artists used it their paintings.
Moreover the golden number appears in biology, for example in
the proportions of many life forms.
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is the ratio of any circle’s circumference to its diameter.
The Greek letter is used because this is the first letter of the
Greek word “perimeter” referring to its use in the formula
perimeter
. William Jones was the first to use the Greek letter
diameter
in this way in 1706.
It is an irrational number, that is to say a number that can’t be
a
written in the form , where a and b are both integers, with b≠
b
Its numerical value truncated to 4 decimal places is: 3.1416.
1
3
is the first known accurate approximation which was used
7
by the Egyptians in the designs of the pyramids.
Archimedes was the first to estimate rigorously that’s why
also named the Archimedes’ constant.
is
Supercomputer calculations have determined over 1 trillion digits
of the decimal representation of .
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