^^Farey sequences, Ford Circles

Diario

mettere in ordine le frazioni con denominatore < 9.

1816 Farey sequences

John Farey speculated that each new entry is the mediant of its neighbours.

Mediante di 2 frazioni wp

Mediante (  n1

d1

  ,  n2

d2

  )  =   n1+n2
d1+d2

1938 Ford circles "absolutely marvellous geometric interpretation of the Farey series" (Ford)

introduced in a  article called "Fractions".
Ford, best known for them.

ref: https://mathshistory.st-andrews.ac.uk/Biographies/Ford/

Stern Brocot tree

 

Links

  1. Frazioni di un segmento. Suddividere un segmento in parti. Da 1 a 10 parti.
  2. Circonferenza tangente a 3 mutuamente tangenti.

Links inet

  1. wp/Farey_sequence
  2. wp/Mediant_(mathematics)
  3. wo/Ford_circle
  4. wp/Successi�_de_Farey  mi sembra nella lingua piu' illustrata
  5. Book. Topology of numbers https://pi.math.cornell.edu/~hatcher/TN/TNpage.html
    Introduces Farey diagram, and Farey sequences.
  6. wp/Triangolo_di_Sierpinski  Sierpiński gasket or Sierpiński sieve
  7. wp/Stern-Brocot_tree

  8. Ani

  9. ford-circles
  10. apollonian-gasket

     

 

Talk

 

  n1   n3     n1+n2
Mediante(
,
  ) =  
  d1   d2     d1+d2