The Steinhaus Cyclus

The Steinhaus Cyclus is 145, 42, 20, 4, 16, 37, 58, 89.

The Concept

Step 1: Take any natural number with four digits.

Step 2: Add the squares of all the digits of the number.

Step 3: Repeat this procedure of adding the squares of the digits of the number.

Step 4: This procedure gives the result either number 1 or 145.

Step 5: After getting the number 1 or 145, the Steinhaus Cyclus keeps on repeating.

For Example

Number 1234

Adding the squares of all the digits of the number 1234 [1² + 2² + 3² + 4² ] => 30

Repeat this procedure:

[3² + 0² ] => 9

[9² ] => 81

[8² + 1² ] => 65

[6² + 5² ] => 61

[6² + 1² ] => 37

[3² + 7² ] => 58

[5² + 8² ] => 89

[8² + 9² ] => 145

[1² + 4² + 5² ] => 42

[4² + 2² ] => 20

[2² + 0² ] => 4

[4² ] => 16

[1² + 6² ] => 37

[3² + 7² ] => 58

[5² + 8² ] => 89

[8² + 9² ] => 145

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As you can see, after getting the number 145, the Steinhaus Cyclus 145, 42, 20, 4, 16, 37, 58, 89 keeps on repeating.

Hope you have understood this amazing concept of the Steinhaus Cyclus. You can try yourself using any other four-digit number. In case of any issue, kindly provide your valuable comments.