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Bonsai and That Pesky Scalene Triangle

by Ron Martin

Ever wonder what all the talk concerning that scalene triangle is all about. Just why is it so important in bonsai. Most of them have more curves than straight lines so why not an oval.

Is that scalene triangle a triangle or just a group of reference points for height, width and depth. A boundary so to speak in which our bonsai is confined. If so why ?

Just how does a tree’s growth pattern relate to that scalene triangle ? How does it make our little bonsai seem so big, so old and massive?

Why, of all things is it so important ?

I have posed some big questions here. The answers to which are not all that complicated but will take more than just a few words to answer.

Surprisingly enough most of the answers have nothing to do with bonsai.

Bonsai is more an art of illusion than anything else. We take something small and try to make it look as big and as old as we can.

Forget art for a bit and lets just go with the illusion. Think about what makes things look big.

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Go to the tallest building you can find. Look up. The walls seem to converge. The top of the building will seem to lean toward you. Look left and right. The sidewalk and the top of the building will start to converge off in the distance.

These are the visual cues that the brain associates with a large object. In bonsai we exaggerate these cues. The angles of our outline are more pronounced. The lean at the top a bit greater.

In bonsai we crunch down a 60 foot tree to a much smaller area. The brain is fooled by the "triangles" we see. What was small is now big.

The answer to the first part of the question is perspective . Or better yet trickery. This has nothing to do with art, just setting the stage. Fooling the brain to think something is bigger.

Are we talking triangles or just converging lines.

All of us have seen that straight road that goes on forever. The edges of that road seems to almost come to a point way off in the distance. We know that the road is a constant 20 feet wide so why does the road appear to be much narrower way off in the horizon.

Our eyes distort the road. Items further away seem smaller. The brain interprets this as distance.

The same thing happens when you look up at a tall object. The sides seem to converge.

This is something we can use to fool the brain. Convince it that our little tree is much larger than it actually is.

Consider the trunk of the bonsai. What is usually desired is a trunk with movement and good taper. Nothing new there. But does that taper make the trunk look taller. Older and more massive. Will increasing that taper make it look taller. Will a drastic taper seem to make it more massive.

The same goes with a branch when viewed from the trunk out.

With trees our brain associates age with size and mass. This taper gives us mass thus perceived age.

Using the same principle and looking upward the brain expects the lower branches to appear longer than those further away.

So now lets fool the senses.

We set the viewer up. We dictate where the eyes go to by adjusting the viewing height of our bonsai forcing the viewers eyes to a point about half way up the trunk of our little tree.

Now that the eyes are there we have all those converging lines radiating out from that spot. Presto, the tree appears taller, more massive. This is trick number one.

One thing to remember though is once I put all these converging lines together to form our bonsai is that I do come up with a triangle of sorts.

So now we are back to the beginning. Just why is that scalene triangle so important.

First and foremost is perspective. Forced perspective at that.

There are other more subtle reasons. The triangle implies:

1. Stability - The triangle is a shape with a wide base and therefore can not be easily knocked over (blown over?). The relativity of this to bonsai should be obvious, age = stability.

2. Scalene - symmetry is also a sign of stability but it does not include a lot of variety and/or interest. In bonsai terms, the symmetrical tree could become a tree by rote rather than a tree of artistic merit. Scalene is NOT symmetrical so avoids that problem but therefore needs stability of the triangle. Therefore a scalene (non-symmetrical) triangle.

3. Implied - By creating a bonsai with just the limits or corners of a scalene triangle evident, the artist requires the viewer to become a participant in the artistic work therefore adding interest for the viewer.

Are there other artistic schemes? Of course! Should all bonsai be forced into the scalene triangle format? Of course not!.

So where does the scalene triangle fit in? As a guideline; as a beginning; as a safety net; as a tool. Just another thing we do to fool the senses into thinking something is bigger than it is.

What goes on in that triangle is the artistic part of the equation. But first we must create the illusion. Give the brain what it needs to think on a grander scale.

Take a photograph of a large tree. Make sure that there is nothing else in that picture that will give one a sense of scale. No cars, buildings, people, etc.

That 60 foot tall tree is now reduced to a 3x5 inch piece of paper. But even in the photo it still looks big.

Another example of this would be a small photograph of a semi-truck. No matter how small the picture is that darn truck still looks massive

Look closely at that photo. Find those converging lines (or triangles if you wish). See how the brain was fooled by that small photo. Now all we have to do is repeat this in our bonsai.

There are other tricks we have to fool the brain. Visual weight is one that comes to mind. But that is a subject much more complex and deserves an article of its own.

The most important thing to remember is that all these tricks are just tools. Just like those scissors ,wire and concave cutters. Nothing more or less.

Like the artist's paint brush, they are just a means to create the art. How these tools are used is up to the artist. But how and when these tools are used will govern how successful you are. Learn not only the "rules" but understand them. Know what results you derive from them. Then select the ones that fit the composition you are working on.

I said previously there is really no such a thing as a scalene triangle used in styling bonsai. Actually there is just a bunch of converging lines. Any time you put a bunch of converging lines together you will get a triangle of sorts.

Truth be know the points of that imaginary scalene triangle are really just reference points.

They set the boundary of the tree. The width and height. Nothing more.

No part of the tree will exceeded these reference points but not all parts of the tree need to extend to the boundary of that "triangle"

As we go from the base of the tree upwards the branches are younger and shorter so naturally everything stays within the confines of the imaginary triangle .

The drawings below shows how most of us were trained to style a bonsai


Points A & C are where the primary branches end (width) and B is the apex (height) . Everything else on the tree falls in there somewhere. They just never exceed those imaginary lines set by A,B & C.

Not a bad way of looking at it but kind of restrictive. There is more to the composition than just the primary branches and an apex.

It leaves out important things like the trunk and the pot just to name a couple of them.

If we change things a bit and consider A,B & C to be just reference points we bring everything into consideration. We can use it just for the tree or a branch. We can even include the pot into the equation. It all depends on how one looks at the "triangle"

By thinking of those points as reference points we can carry styling to the next level. We can see the whole composition.

Lets start by laying that "triangle" down.




Now those reference points show width and depth.

This is the way I like to visualize the tree. I first take care of width and depth. Normally these points are the primary branches. Now I head upwards.

I know that the further up I go the younger the branches are and therefore smaller and shorter. No need to consider the upright reference points. That will naturally now take care of itself. The base will define the height simply by the length of the branches as I move upwards. Sooner or later the branches will form the apex. What is above that will be cut off .

By simply looking at those reference points in a bit of a different way I have forced myself to see the tree in three dimensions.  Easy, isn't it!

As I said in the beginning there is really no scalene triangle in bonsai styling. Just a bunch of converging lines.

The tapering trunk is a set of converging lines. So are the tapering branches. The overall outline of the tree will also be a set of converging lines.

This is what will show perspective. It is what makes our little tree seem so much bigger. How all those converging lines are put together is what makes for a good bonsai.

An informal up-right seems to be the most popular style in bonsai today. Guess that has a lot to do with the fact that it is also the style most found in the natural world.

When I look at that style of tree the first thing I really need to see is the shape of the trunk. It has to look more or less like an elongated “S”

On that “S” turn we establish the confines of our tree.

Laying that triangle flat forces us to think in three dimensional terms.

Normally the lower primary branches are used to establish the width and depth of the tree.

Not wanting to stray too far from the norm lets do just that. Those dotted lines will be our primary branches.

So now we have somewhat of a plan. We know the style of tree that we want to do.

Now go back to that “S” shaped trunk






Add branches. Since we want the branches to be on the outside of a turn the placement is easy

Now lets start adding some converging lines to our composition.

A bit of taper to the trunk.

Mustn’t forget the branches. They also need to have taper.

Foliage pads on those branches will also need a bit of taper. Thicker near the trunk and thinner at the tip of the branches.

As we work our way up the tree the branches become shorter and more numerous. Eventually they will terminate in an apex.

A few more converging lines and we have a nabari

The left and right branch give us width and that branch going to the rear gives us depth.

With all the converging lines in our little drawing I would be surprised if one could not find at least one or two triangles.

Better to forget the triangles though and just consider the reference points. These points can take in the whole composition , be adjusted to fit a single branch or just the trunk. It all depends on what part you are working on.

It also opens up the mind to other possibilities.

Lets go back to that informal-upright.

The width of the tree is defined by those two lower branches. What would happen if one of those branches went away.

Kind of a lopsided affair now isn’t it.

But what would happen if we expanded our references to include a pot. In this case a scoop pot.

Now we are no longer lopsided. The tip of the pot becomes the right side of the composition. Between the tip of the branch on the left and the tip of the pot on the right we now have width defined again.

So now where does all this lead us to. How can we use all this stuff to style any bonsai.

Not a bad question but, one that requires , naturally , a whole lot of words. A whole new story ;o)


Illustrations by: Carl L Rosner

No re-printing of this material authorized without the authors permission.

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