Piero della Francesca, Convenerunt in unum, supporting David King’s interpretation (see the article „A Leap of Faith“ in „Nature“ 29 March 2007) / © Franz Gnaedinger 1991/2007 www.seshat.ch  fg(a)seshat.ch  fgn(a)bluemail.ch


gia19.JPG / gia20.GIF / gia21.JPG / gia22.JPG


conv01.JPG / conv02.GIF / conv03.GIF / conv04.GIF / conv05.GIF / conv06.GIF / conv07.GIF / conv08.GIF / conv09.GIF / conv10.GIF / conv11.GIF / conv12.GIF / conv13.GIF / conv14.GIF / conv01.JPG




Piero della Francesca, Baptism of Christ, picture, geometry (square, grid 12 by 12, lower circle of Christ, pyramid of Christ, upper circle of Holy Spirit present in a dove), geometry applied to the picture:   gia19.JPG / gia20.GIF / gia21.JPG / gia22.JPG


Piero della Francesca, Convenerunt in unum (Flagellation of Christ)   conv01.JPG


Frame 24 by 18 units, format 3/4, grid 20 by 14 units   conv02.GIF / conv03.GIF


Braccio Fiorentino 58.36 cm; proposed unit for Piero’s painting 1/16 braccio or 3.6475 cm; frame 65.655 by 87.54 cm or 9/8 by 3/2 bracci Fiorentini.


The picture is slightly larger than the grid 14 by 20 – observe the thin strips under and above the grid:   conv04.GIF


Grid applied to the picture, yellow dot: center of perspective, red dot: center of grid, blue dot: center of small picture within the picture:   conv05.GIF


Small picture within the picture, 12 by 12 units, area 144 square units, one third of the area of the picture and frame together (18 x 24 = 432 square units):   conv06.GIF / conv07.GIF


Diagonals of the square 12 by 12:   conv08.GIF


Geometry applied to the picture:   conv09.GIF


The vertical lines of Christ and cardinal Bessarion divide the length of the picture into 7 plus 6 plus 7 units, the length of the frame into 9 plus 6 plus 9 units or in the ratios 3/8 and 5/8 (approximating the golden section). The diagonal connecting the bottom right corner of the left field 14 by 7 with the top left corner of the right field 14 by7 is hold by the Roman. Geometry applied to the picture:   conv10.GIF / conv11.GIF / conv12.GIF


Left square 14 by 14 plus diagonals, right field 14 by 7 plus diagonals, applied to the picture:   conv13.GIF / conv14.GIF



The geometrical examination of Piero’s painting confirms David King’s fine interpretation and suggests a modification as well: Piero came first, the inscription on the astrolabium for Cardinal Bessarion second. One may assume that Regiomontanus was a good friend and informal pupil of Piero della Francesca, well acquainted with the picture, whereupon he encoded not only the names but also some of the crucial numbers of the painting into the inscription on the astrolabium honoring Cardinal Bessarion:


   length of grid 20 units –– 20 letters in the first line


   height of frame 18 units –– 18 letters in the second line


   from right side of frame to line of Christ,

   from left side of frame to line of Bessarion

   15 units each –– 15 letters in the third line


   height of grid 14 units, big square 14 by 14 ––

   14 signs in the last line (count    as one sign)


   SUB  DIVI  BESSARIONIS  DE  ––  20 letters

   CARDINE  DICTI  PRASEI  ––  18 letters

   DIO  ROMAE  SURGO  IO  ––  15 letters

   ANNIS  OPUS  :–  1062  ––  14 signs


For the interpretation of the couplet see David King. Here just one addendum. The lines of Christ and Bessarion divide the length of the picture into 7 plus 6 plus 7 units. Divide the first line accordingly and you get  


   SUBDIVI   BESSAR  IONISDE     7+6+7 letters


Sub divine Bessarionis ‘under the divine Bessarion’ becomes




subdivide, a pun by the astronomer and mathematician Regiomontanus who transformed the painting by his presumed friend and informal teacher Piero della Francesca  conv01.JPG  into a dedication to Cardinal Bessarion, encoding both names and numbers of the painting.





Geometry in art, John the Baptist (reconstructions and interpretations)   gia.htm