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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 ?.

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A MAGIC FORMULA OF Nature

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  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

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