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Number 153: number of the fish
1. Number 153: number of the fish
Start with four points (on the same line) that create three equal line segments.
2. Upper circle
At the higher of the two interior points, draw a circle with radius equal to one line segment.
3. Lower circle
At the lower of the two interior points, draw a circle with radius equal to one line segment.
4. Both circles
The two circles create on intersection area that is often seen in Venn diagrams.
This intersection area was called a mandoria in Latin (and Italian), meaning almond (that is, "
a mandoria") because if its shape.
5. Latin terms
This intersection area was also called
vesica pisces.
The Latin word "vesica" ≈ "bladder" (think of a football shape sometimes called an "oblate spheroid").
The Latin word "pisces" ≈ "fish", which is related to the English word "fish" and the German word "Fische" ≈ "fish", following Grimm's Law where the "p" and "f" are related from a common ancestor.
The vesica pisces shape appears often in Medieval art.
6. Equilateral triangles
In the intersection area, two equilateral triangles can be drawn. Euclid proved that these are equilateral triangles. From geometry and the Pythagorean theorem, the width of the fish (height of the equilateral triangle rotated) can be determined. For more on this, see
Height of a regular triangle .
7. Fish symbol
By appropriate drawing, a representation of a fish can be created.
8. Number 153: number of the fish
This fish shape was adopted by early Christians as the symbol of Christianity (about 100 AD), but the symbol itself goes back many hundreds of years.
Pythagoras (about 500 BC)
Euclid (about 300 BC)
Archimedes (about 200 BC)
The number
153 was known as the "
number of the fish".
9. Christian fish shape
10. Fish body ratio
The intersection area of this fish shape has a width and a height. The ratio of the width to height is as follows, as was proven by Pythagoras (including the approximation).
11. Number 153
The approximation ratio is
265/153 and the number
153 was called the "
number of the fish". For more on approximation ratios, see
Non-rational number approximation .
Why the number
153 and not the number
265? One reason might be that the number
153 has many other interesting properties (many more so than
265).
12. Sum of cubed digits
Each digit of
153, when cubed and added, sums to
153.
Such a number is called a
narcissistic number.
13. Triangular number sum
The sum of the integers from
1 to
17 is
153.
For more information, see the following:
Triangular numbers .
14. Factorial number sum
The sum of the factorials from
1 to
5 is
153.
For more information, see the following:
Factorial function .
15. Sum of squares
The number
153 can be represented as the sum of two squares.
16. Hexagonal number
The number 153 is a hexagonal number.
... more to be added ...
17. End of page
