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I received from Mr. Joshua Gottdenker the message in 2011 that he wants to make a model of shape similar to the spherical spiral onto an egg instead of a sphere. Then, I make an equation of spiral on egg surface under the collaboration and instruction given by Mr. SuugakuDokugakujuku Jukuchou (whose correct name is Mr. Yasuyuki ASAI), and obtain the coordinates data of the spiral by computer calculation.
Soon after I sent the date written in an Excel file to Mr. Joshua and also to Mr. Svein Daniel Solvenus who is contact to me in chance at the same time, they create several 3D figures of both egg and apple, and send me them.

with the use of Eqs.(5) and (6) 
with the use of Eqs.(5) and (6) 
with the use of Eqs.(5) and (7) 
with the use of Eqs.(5) and (7) 
3. Spiral on an Apple Surface
Though the equation of apple shaped curve in (x, y) plane is given in the Eq.(3) in the page of "apple shaped curve", it is written as the following to give a spiral on an apple surface in the same process to Eqs.(1) and (2).



with the use of Eqs.(3) and (8) 
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