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Number 153: number of the fish
by RS  admin@robinsnyder.com : 1024 x 640


1. Number 153: number of the fish
Line segmentsStart with four points (on the same line) that create three equal line segments.

2. Upper circle
Circle 1At the higher of the two interior points, draw a circle with radius equal to one line segment.

3. Lower circle
Circle 2At the lower of the two interior points, draw a circle with radius equal to one line segment.

4. Both circles
CirclesThe 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 vesica pisces shape appears often in Medieval art.

6. Equilateral triangles
TrianglesIn 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
FishBy appropriate drawing, a representation of a fish can be created.

8. Number 153: number of the fish
FishThis 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. The number 153 was known as the "number of the fish".

width to height of fish

9. Christian fish shape
FishOnly

10. Fish body ratio
Fish ratioThe 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).

width to height of fish

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.

Sum of cubed digits of 153
Such a number is called a narcissistic number.

13. Triangular number sum
The sum of the integers from 1 to 17 is 153.

Triangular number sum of 153
For more information, see the following: Triangular numbers .

14. Factorial number sum
The sum of the factorials from 1 to 5 is 153.

Factorial number sum of 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.

Sum of squares yielding 153

16. Hexagonal number
The number 153 is a hexagonal number.

... more to be added ...

17. End of page

by RS  admin@robinsnyder.com : 1024 x 640