1 / 57

A MAGIC FORMULA OF Nature

A MAGIC FORMULA OF Nature. Primo Brandi - Anna Salvadori. Riccione 2018. Mathematics & Real life. www.matematicaerealta.eu. The description of the forms is one of the major problems of biology . Is mathematics able to give a support ?.

jory
Télécharger la présentation

A MAGIC FORMULA OF Nature

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A MAGIC FORMULA OF Nature Primo Brandi - Anna Salvadori Riccione 2018

  2. Mathematics & Real life www.matematicaerealta.eu The descriptionof the formsisoneof the major problemsofbiology. Ismathematicsabletogive a support? Mathematicsis the languageof Science and Tachnology Anna Salvadori – Univ.Perugia Riccione 2018

  3. Mathematics & Real life www.matematicaerealta.eu Johan Gielis(American Journal of Botany 2003) proposed a formula that can describe a wide rangeofnaturalshapes Anna Salvadori – Univ.Perugia Riccione 2018

  4. Gielissuperformula Bottom up: todiscover the themain idea behind Top down: tounderstand the roleofeachparameter Anna Salvadori – Univ.Perugia Riccione 2018

  5. Gielissuperformula Bottom up: todiscover the themain idea behind Productoftwofunctions Anna Salvadori – Univ.Perugia Riccione 2018

  6. Gielissuperformula Bottom up: todiscover the themain idea behind Letus concentrate ourattempition on the secondfunction assumingconstant the first one Anna Salvadori – Univ.Perugia Riccione 2018

  7. Gielissuperformula Bottom up: todiscover the themain idea behind Assume the threepowerparameters coincide Anna Salvadori – Univ.Perugia Riccione 2018

  8. Gielissuperformula Bottom up: todiscover the themain idea behind Assume the threepowerparameters coincide Anna Salvadori – Univ.Perugia Riccione 2018

  9. Gielissuperformula Bottom up: todiscover the themain idea behind Equivalentformulation Anna Salvadori – Univ.Perugia Riccione 2018

  10. Gielissuperformula Bottom up: todiscover the themain idea behind Anna Salvadori – Univ.Perugia Riccione 2018

  11. Gielissuperformula Bottom up: todiscover the themain idea behind Re-scale the variable Anna Salvadori – Univ.Perugia Riccione 2018

  12. Gielissuperformula Bottom up: todiscover the themain idea behind Re-scale the variablem=4 Anna Salvadori – Univ.Perugia Riccione 2018

  13. Gielissuperformula Bottom up: todiscover the themain idea behind Frompolartocartesiancoordinates Anna Salvadori – Univ.Perugia Riccione 2018

  14. Gielissuperformula Bottom up: todiscover the themain idea behind Frompolartocartesiancoordinates Anna Salvadori – Univ.Perugia Riccione 2018

  15. Gielissuperformula Bottom up: todiscover the themain idea behind Re-scale the twoviariablexa=b=1 Anna Salvadori – Univ.Perugia Riccione 2018

  16. Gielissuperformula Bottom up: todiscover the themain idea behind Wellknownequation key idea Anna Salvadori – Univ.Perugia Riccione 2018

  17. Mathematics & Real life www.matematicaerealta.eu Botton up: todiscover the themain idea behind Top down: tounderstand the roleofparameters Anna Salvadori – Univ.Perugia Riccione 2018

  18. Gielissuperformula Bottom up: todiscover the themain idea behind Letus start from the key idea Anna Salvadori – Univ.Perugia Riccione 2018

  19. The squared circle Lamé circumference Gabriel Lamé(1795 –1870) revolutionized this view Anna Salvadori – Univ.Perugia Riccione 2018

  20. The squared circle Lamé circumference For a long time the circle and the square have been considered as "opposed" figures. Gabriel Lamé(1795 –1870) revolutionized this view Anna Salvadori – Univ.Perugia Riccione 2018

  21. The squared circle Lamé circumference For a long time the circle and the square have been considered as "opposed" figures. Gabriel Lamé(1795 –1870) revolutionized this view Anna Salvadori – Univ.Perugia Riccione 2018

  22. The squared circle Lamé circumference For a long time the circle and the square have been considered as "opposed" figures. Gabriel Lamé(1795 –1870) revolutionized this view Euclidean LinfinutyMAX L1 Manhattan p=0 0<p<1 p=1 1<p<2 p=2 p>2 p->infinity Anna Salvadori – Univ.Perugia Riccione 2018

  23. Super ellipses In the real life PietHein(1959) Sergel's Torg, Stockholm Anna Salvadori – Univ.Perugia Riccione 2018

  24. Super ellipses In the real life PietHein(1959) Sergel's Torg, Stockholm Anna Salvadori – Univ.Perugia Riccione 2018

  25. Super ellipses In the real life PietHein(1905-1996) glasses, plates, desk lamps … Anna Salvadori – Univ.Perugia Riccione 2018

  26. Super ellipses In the real life bamboo cane Anna Salvadori – Univ.Perugia Riccione 2018

  27. First step to superformula From Cartesian to Polar coordinates Anna Salvadori – Univ.Perugia Riccione 2018

  28. First step to superformula From Cartesian to Polar coordinates Rodonee Grandi’s roses Luigi Guido Grandi (1671-1742) Anna Salvadori – Univ.Perugia Riccione 2018

  29. First step to superformula From Cartesian to Polar coordinates Anna Salvadori – Univ.Perugia Riccione 2018

  30. First step to superformula From Cartesian to Polar coordinates Anna Salvadori – Univ.Perugia Riccione 2018

  31. First step to superformula From Cartesian to Polar coordinates represent the length of the vector ray corresponding to angle the local minima and maxima play a fundamental for the figure shape Anna Salvadori – Univ.Perugia Riccione 2018

  32. First step to superformula From Cartesian to Polar coordinates represent the length of the vector ray corresponding to angle the local minima and maxima play a fundamental for the figure shape They correspond to the minimum and maximum points of the reciprocal function Anna Salvadori – Univ.Perugia Riccione 2018

  33. First step to superformula From Cartesian to Polar coordinates represent the length of the vector ray corresponding to angle the local minima and maxima play a fundamental for the figure shape They correspond to the minimum and maximum points of the reciprocal function Anna Salvadori – Univ.Perugia Riccione 2018

  34. First step to superformula From Cartesian to Polar coordinates Functions admits 4 minimum points and 4 maximum points for every value of parameter p Anna Salvadori – Univ.Perugia Mathenjeans 2018

  35. Second step to superformula Fase parameter Anna Salvadori – Univ.Perugia Riccione 2018

  36. Second step to superformula Fase parameter m integer m=2 m=1 m=3 m=4 m=5 m=6 m=20 m=10 Anna Salvadori – Univ.Perugia Riccione 2018

  37. Second step to superformula Fase parameter m rational m=5/3 m=1/2 m=3/2 2 spins 2 spins 3 spins Anna Salvadori – Univ.Perugia Riccione 2018

  38. Second step to superformula Fase parameter m irrational m=e 3 spins 7 spins 14 spins Anna Salvadori – Univ.Perugia Riccione 2018

  39. Third step to superformula Power Parameters pi The number of possible shapes increase greatly assuming different values for the exponents Each parameter produces the effect of a non-linear transformation. Anna Salvadori – Univ.Perugia Riccione 2018

  40. Third step to superformula Power Parameters pi Anna Salvadori – Univ.Perugia Riccione 2018

  41. The superformula Two remarkable particular cases: Anna Salvadori – Univ.Perugia Mathenjeans 2018

  42. The superformula Two remarkable particular cases: Anna Salvadori – Univ.Perugia Riccione 2018

  43. The superformula First case: spirals Anna Salvadori – Univ.Perugia Riccione 2018

  44. The superformula Two remarkable particular cases: Anna Salvadori – Univ.Perugia Riccione 2018

  45. The superformula Second case: flowers Anna Salvadori – Univ.Perugia Riccione 2018

  46. The superformula Anna Salvadori – Univ.Perugia Riccione 2018

  47. The superformula The code Anna Salvadori – Univ.Perugia Riccione 2018

  48. Code – computer graphic Classiscartoons Anna Salvadori – Univ.Perugia Riccione 2018

  49. Code – computer graphic Computer images Anna Salvadori – Univ.Perugia Riccione 2018

  50. Code – computer graphic Anna Salvadori – Univ.Perugia Riccione 2018

More Related