# Plant Care and Trigonometry

My Mom recently explained to me how to tell if an aloe plant needs to be watered:  if there isn’t enough water in the surrounding soil, the roots will draw water down from the stalks.   As water is drawn down, the stalks will start to sag, kind of like a hot-dog balloon losing air.

This got me thinking that there may be a formula that relates the angle an aloe stalk makes with the normal to the ground and its percent water capacity–perhaps involving cosine?  The basic idea is that as percent water capacity decreases, the angle with the normal increases.

Categories: Appreciation

#### patrick honner

Math teacher in Brooklyn, New York

#### Mr Xiao · July 7, 2010 at 3:14 pm

Interesting idea, but there are too many others factors come to play with the angle formed by its leaf and the ground.
The angle can change due to the the newly growing leaves. They force the outer layers leafs to bend.
I imagine when aloe is saggy, its leaves are curved.Where do you the angle measurement. The tip of the leaf of or the bottom? (tip have bend down a lot, while the bottom changes a little.) Are you planning on using Calculus to find the slope of the curve?
It can also be the case that:
Lets say aloe leave can hold 100% of water, but it only becomes saggy when its water content has fallen to 50%. The angle formed can’t be used here.
I learned a new word today: sag
😀

#### Sam Kolins · July 7, 2010 at 5:15 pm

While I think investigating this topic might be extremely difficult in some areas considering all the various required factors, I wouldn’t be surprised if there was some mathematical relationship that could be drawn out here.

It’s easy to name a dozen or so examples of the Fibonacci sequence in nature, so I’m fairly certain trigonometry has something to show for itself in nature as well. 🙂

We learn a lot from nature.

#### mrhonner · July 8, 2010 at 9:14 am

A lot of good questions are raised about measuring the angle of the aloe stalk. Indeed, as days pass, the stalk starts to curve–so maybe it is more realistically a calculus question. It kind of looks like a parabola now.

#### dhc · July 10, 2010 at 12:11 am

I don’t think you need to make it harder than it is (trigonometry, calculus, parabolas). You can just measure the angle as if the leaf were straight (measure from tip to base). The fact that they are curved should not make a big difference. If you really want to focus on the curvature of the aloe, then you can measure the length of the arc and find the radius. Record your observations regularly and you should find a pattern (the radius may decrease).

The difficult thing, I think, is measuring the water content or percent-capacity of the aloe because some of it evaporates or gets absorbed. So it would be hard to keep track of how much water is left.

Something else that interested me about this post was that I’ve always wondered if it was better to water plants directly or to water the soil. If aloe needs water in the soil, then it would be best to water the soil rather then the leaves themselves, since (I think) the leaves are waterproof and easily evaporated (especially in this weather).

And I wonder if the rate at which plants use up water is linear or exponential (or neither)

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