By ROBERT DRYJA
Holmes now was particularly restless as a result of two events. First, he had just deduced that a particular diamond was a copy due to the angles of its facets. The angles had not matched the angles of the genuine article. Second, it was summer and he wanted to conduct his weekly explorations of the Jemez Mountains. I anticipated he would make some connection between geometry of the diamonds and what he observed as we hiked along a trail.
The case of the Geometric Dandelion. Courtesy photo
“My interest this week is in the recovery of plant life along the Valle Grande trail following the forest fire. We will hike from areas that had intensity burns to areas hardly affected at all. What will things look like in the transition between the two?” And so we were off to the trail.
“Holmes, this is remarkable.” This transition area is a field of dandelions.”
“Correct Watson.” Enough of the trees in the transition area have survived the fire to provide a level of shade that is conducive to the grown of dandelions. Note that few are growing in the completely shaded unburnt areas or the sunny completely burnt areas.”
Dandelions along the Valle Grande trail. Photo by Robert Dryja
“It’s time for some close observations.” Holmes then was down on his knees, a magnifying glass and tweezers at the ready.
“Ah, there are several kinds of geometry present.” Holmes had selected a dandelion that was on the verge of releasing its many seed florets.
“Note the overall shape. All the florets together are creating an almost perfect sphere. Also note that the angles among any three adjacent florets are almost the same. A dandelion creates 45 degrees angles while growing its seeds.”
“This reminds me. The copy of the diamond had equal angles for all of its facets unlike the original diamond. The original had 45 and 30 degree angles.”
A sphere of florets and the triangular spacing among adjacent florets. Photo by Brian Johnston
Holmes then removed florets from one side of the sphere. He did this with a gentle puff of his breath.
“Interesting. We now have an ellipse shape when observing a floret from the side. An ellipse shape is maintained even when the distance between florets changes.”
“Holmes,” I said. “It becomes more interesting when you look at the base where all the florets originate.”
“Excellent observation,” Holmes said. “We now see an ellipsoid. An ellipse in three dimensions if you will.”
“Remarkable,” I said. “The bases of the florets are aligned in parallel and create ellipses along the greater and shorter axes of the ellipsoid.”
Florets creating ellipses when seen from the side. Photo by Robert Dryja
The ellipsoid base for the florets. Photo by Robert Dryja
Parallel points along the minor and major axes of the ellipsoid base. Photo by Brian Johnston
Holmes became reflective as we returned from the Valle Grande trail. “How different Taraxacum officinale becomes when seen in forest. It usually is seen as a nuisance weed when growing in a yard. However it is an amazingly complex mathematical object of beauty when observed in the forest.”
What to personally observe a dandelion or other plants with a microscope? Then bring your specimen to the Los Alamos Nature Center to use its projection microscope.