Bernoulli's Spiral

Jacob Bernoulli was born in Basel, Switzerland. As a young man, he studied theology and entered the ministry.  Later he studied mathematics and astronomy.   Traveling throughout Europe from 1676 to 1682, Jacob learned about the latest discoveries in mathematics and the sciences.[1]First described by RenéDescartes, Bernoulli extensively investigated the logarithmic spiral.   “This equiangular spiralor growth spiralis a special kind of spiral curve which often appears in nature.”[2]  Jacob called it Spira mirabilis, “the marvelous spiral”.  

Meditation
Hebrews 1:10—And: In the beginning, Lord, You established the earth, and the heavens are the works of Your hands.
 
There is an deliberate order to creation.  By investigating what fascinated Bernoulli, we discover God’s calculus at work.  Any progression which turns or twists at a constant rate but grows or moves with steady acceleration will generate a logarithmic spiral.  The following are examples of such spirals in nature:·              

A hawk’s circular approach to its prey.  This raptor’s angle of flight is the same as the spiral’s pitch.
·   An insect’s approach to light. 
·   The natural growth curves of plants.
·  The arms of spiral galaxies.  The Milky Way has multiple spiral arms each with a logarithmic spiral pitch of about 12 degrees. 
·   The cornea nerves in our eyes.
·   The horns of many bovids like gazelles.
·    The arms of tropical cyclones (hurricanes).
·    The shells of mollusks and nautilus shells
·   Beaches formed as a result of wave refraction and diffraction by the coast.  A good example of this is Half Moon Bay in California.[3]  

Did you know that engineers discovered that the optimal curve for highway turns is a logarithmic spiral? God’s arrangement of sunflower seeds in the sunflower and work with the cactus, further reflect His artistic formula. The Creator who took the time to meticulously plan the heavens and earth reveals how much He loves us!  Consider that the human embryo reveals an equiangular spiral.  From our designed beginning we grow unique in appearance, personality and thought.  And the Father who takes splendor in shells, finds greater satisfaction in our souls—something to think about . . . in reveration!   

Inspiration
Jacob Bernoulli was so enthralled by “the equiangular spiral’s self-reproducing properties, that he had had the curve engraved on his tomb with the phrase “Eadem mutata resurgo” (Though changed, I rise again the same.)”[4]  
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©2012 Daniel York  ARR. Reveration is the weekly devotional ministry of First Cause.  If you would like to receive these devotionals go to www.firstcause.org and click on the “Click here to receive weekly devotionals” box.  Unlimited permission to copy this devotional without altering text or profiteering is allowed subject to inclusion of this copyright notice.      
 
Ecclesiastes 12:10-The Teacher sought to find delightful sayings and to accurately write words of truth.  (Holman CSB)
 

 

[1]http://en.wikipedia.org/wiki/Jacob_Bernoulli
[2]http://en.wikipedia.org/wiki/Logarithmic_spiral
[3]Ibid
[4]http://online.redwoods.cc.ca.us/instruct/darnold/calcproj/fall98/darrent/equiangularspiral.html