Car Talk Landscape Architecture Puzzler

This week’s Car Talk puzzle as described by Ray:

This puzzler is from my horticultural and mathematical series. It was sent in by Daniel Reiss. And, of course, I couldn’t resist the temptation to mess with it a little bit.

Here it is.

An eccentric billionaire decided to interview landscapers for his newly constructed estate. Part of the interview was a simple test. He said:

‘Four is my lucky number. I made my fortune working four hours a week, just like those two knuckleheads on Car Talk!

‘So, I want every tree and bush and shrub you plant to be in groups of four. Got it? But in addition, I want each of these four things that you plant, to be the same distance from one another.

‘For example, if you plant four rhododendron, I want them all to be equidistant, i.e., each one is the same distance from each of the other three.’

The question is, can it be done?

Or… you can listen to the audio version, which I prefer!  Though I USUALLY download podcasts of the whole show!

I thought of the answer in less than a second, but don’t ask me how long it took me to MODEL it!

The way that I think about it… Imagine a methane molecule, CH4. The hydrogen atoms become the four trees and the carbon atom (not represented in the model) is invisibly floating between the triangular pool and the cantilevered mezzanine. (Bond angles, 109.5°! Yay!!!)  In the scale model below, each tree is 50 feet away from each of the other 3 trees.

Someone PLEASE tell me if there’s a way to use polar coordinates in SketchUp!  The pyramid took forever for this SketchUp newbie (ie, me!) to accurately model!

I’ll tell you how the tree is growing on the upper level if you tell me how these trees are growing on this MVRDV structure below. My classmates (below) and I were biking around the Netherlands last summer exploring architecture and landscape architecture projects! This Parkrand Building project is in Amsterdam.

Yeah, yeah…  I’ll decrease my chance of “winning” by posting this…  But I didn’t really do this to “win” anyways.  When else are methane bond angles going to be relevant to landscape???  😀

P.S. Do the terms “bush” and “four rhododendron” bother anyone else?  Or is that just me???

6 Responses

  1. Backside attack in the SN2 position!!! Okay, I don’t really remember what that means… It was a nerdy joke that I no longer understand! Nor do I really care to remember… Evil, evil orgo! (orgo = organic chemistry)

    Okay, I just looked it up… And now I’m having all of these bad flashbacks! Nucleophiles… Valence electrons… Sp3 orbitals… Blech!!!

  2. So, the on-air answer mentioned planting that fourth tree on top of a hill… Which actually was the first image that came to my mind after reading the problem statement.

    But I didn’t like that answer, especially after starting to model it. That’s a steep angle of repose!!! Mr. Billionaire would have a difficult time walking straight up the hill. He’d probably have to go up and around… up and around… and wind his way up the hill. Or build a funicular! Fun!

    And he wouldn’t be able to get a standard riding lawn mower up that hill to mow the grass! If he had grass on his hill. Of course with his billions he could indulge in non-standard, inefficient practices.

    And even if the tetrahedron is scaled down to plant smaller plants, that’s still a steep angle! (Because, obviously, the angles are the same at any scale.) He would probably need some sort of structural support to hold the soil to maintain those tetrahedral angles and support the plant at the top of the hill and its roots.

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