# Leonardo’s Formula Explains Why Trees Don’t Splinter

May 20th, 2015
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The graceful taper of a tree trunk into branches, boughs, and twigs is so familiar that few people notice what Leonardo da Vinci observed: A tree almost always grows so that the total thickness of the branches at a particular height is equal to the thickness of the trunk.

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BiologybiophysicsForcesphysicsFOLLOWWIREDTwitterFacebookRSSLeonardos Formula Explains Why Trees Dont SplinterBYSCIENCENOW11.15.11|10:30 AM|PERMALINKShare on Facebook2inShareBy Kim Krieger,ScienceNOWThe graceful taper of a tree trunk into branches, boughs, and twigs is so familiar that few people notice what Leonardo da Vinci observed: A tree almost always grows so that the total thickness of the branches at a particular height is equal to the thickness of the trunk. Until now, no one has been able to explain why trees obey this rule. But a new study may have the answer.Leonardos rule holds true for almost all species of trees, and graphic artists routinely use it to create realistic computer-generated trees. The rule says that when a trees trunk splits into two branches, the total cross section of those secondary branches will equal the cross section of the trunk. If those two branches in turn each split into two branches, the area of the cross sections of the four additional branches together will equal the area of the cross section of the trunk. And so on.Expressed mathematicall

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