The idealistic values of eight important digits from ancient and medieval measures

The

« idealistic French digit »

equals

20, 321 280

nanometres

=

2

10

×  3

4

×  5

1

×  7

2

i.e. a  7-smooth number.

The

« idealistic Austrian digit »

equals

19, 756 800

nanometres

=

2

8

×  3

2

×  5

2

×  7

3

i.e. a  7-smooth number.

The

« idealistic English digit »

equals

19, 051 200

nanometres

=

2

6

×  3

5

×  5

2

×  7

2

i.e. a  7-smooth number.

The

« idealistic Egyptian digit »

equals

18, 900 000

nanometres

=

2

5

×  3

3

×  5

5

×  7

1

i.e. a  7-smooth number.

The

« idealistic Viennese digit »

equals

18, 662 400

nanometres

=

2

10

×  3

6

×  5

2

 

 

i.e. a  5-smooth number.

The

« idealistic Roman digit »

equals

18, 522 000

nanometres

=

2

4

×  3

3

×  5

3

×  7

3

i.e. a  7-smooth number.

The

« idealistic Nippur digit »

equals

17, 287 200

nanometres

=

2

5

×  3

2

×  5

2

×  7

4

i.e. a  7-smooth number.

The

« raw Nippur digit »

equals

17, 280 000

nanometres

=

2

10

×  3

3

×  5

4

 

 

i.e. a  5-smooth number.

With ancient measures, a lack of precision ± 0.17% is normal. However, many nations preserved their measures with high-level accuracy.

Examples:

Beside :  The Austrian foot is identical to the ancient, greek pous metrios, 16/15 Roman foot.

The English compromise foot (1959) is 304.8 mm, exactly one. Compared to the idealistic value of 304.8192 mm, that's 99.9937 %, i.e. - 0.0063 %.

The Austrian klafter (1756-1871) is 1896.6139 mm. Six idealistic Austrian feet are 1896.6528 mm. This is a precision of 99.9979 %, i.e. - 0.0021 %.

French metrologists were obviously mediocre :  French foot (1799)  was 9, 000 000 ÷ 27 706 mm, about 324.839 385 mm. 99.9074 %, i.e. - 0.0926 %.

Above, the term « idealistic Viennese foot » is slightly inaccurate, since 298.5984 mm are really a « komma decreased idealistic Viennese foot ».