The Geometry of the Epeira's Web 



with its own simplicity alone. I count a score 

 of whorls which gradually decrease until they 

 vanish in the delicate point. They are edged 

 with a fine groove. 



I take a pencil and draw a rough generat- 

 ing line to this cone; and, relying merely on 

 the evidence of my eyes, which are more or 

 less practised in geometric measurements, I 

 find that the spiral groove intersects this gen- 

 erating line at an angle of unvarying value. 



The consequence of this result is easily 

 deduced. If projected on a plane perpendic- 

 ular to the axis of the shell, the generating 

 lines of the cone would become radii; and the 

 groove which winds upwards from the base 

 to the apex would be converted into a plane 

 curve which, meeting those radii at an unvary- 

 ing angle, would be neither more nor less than 

 a logarithmic spiral. Conversely, the groove 

 of the shell may be considered as the projec- 

 tion of this spiral on a conic surface. 



Better still. Let us imagine a plane per- 

 pendicular to the axis of the shell and passing 

 through its summit. Let us imagine, more- 

 over, a thread wound along the spiral groove. 

 Let us unroll the thread, holding it taut as we 

 do so. Its extremity will not leave the plane 



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