Do Plants Do Maths?
Introduction: Do Plants Do Maths?
Nature is awesome! There are tons of things that we can not explain in an easy way, like the hidden patterns that are a constant in many different organisms in completely different environments. Things without an obvious relationship or connection but behave in the same specific way.
Scientist have to use their most powerful tool to explain this behavior, and that is Mathematics. When using "math lenses" you can describe these complex patterns with constants, and there is one that shines above them all (at least in nature behavior) and it´s called the Golden ratio. I have uploaded pictures of plants which patterns can be described with this constant.
With the Codeblock addition in Tinkercad is now possible to simulate how a sunflower spread its seed in the most optimum way, yes with the golden ratio.
This is a great opportunity to explore mathematics, geometry, rational numbers, design, and more. This is a really cool STEM class for your high school students.
If you want to play a little bit with this in advance, you can see a series of cool videos of Vihart (vihart.com) starting with the part one here:
Now lets prepare everything for our code, so I will take advantage of this instructable to make a mini tutorial on how to use codeblocks in Tinkercad to create a sunflower. Then I will proceed with its seeds and the golden ratio simulation.
So let´s begin.
Step 1: Create a Sunflower With Tinkercad Codeblocks (Creating One Leave)
Codeblocks is simple to use once you get the hang of it. If you know how to use Tinkercad 3D designs app this will be even easier because it will be just translate what you normally do with codes. If you haven´t used Tinkercad before, you can go there and follow a quick and sufficient tutorial to understand how it works. You can even jump this and go with codeblocks right away, there is a basic tutorial of how to use it too.
Let´s create a leave.
For any 3D design you just have to merge different shapes in order to create a more complex one. So, for me a sunflower leaf has a teardrop shape, and one way to create this is merging a cylinder and a roof, two of the basic shapes offered in Tinkercad. So let´s code this.
Select and drag a Cylinder block from the "shape" menu (blue). In the block, there are some parameters you can modify to change the shape. In this case I changed the color to yellow (the color of the leaf) and the radius to 4 and the height "H" to 3. 389
This two parameters are the ideal size for this exercise. In any other application you can modify them to fit whatever you want to achieve. ----Check the first image.
Next, select and drag from "shape" (blue blocks in menu) the roof block. Change the color to yellow and the length "L" to 3 to match the "H" of the cylinder. ----Check the second image.
NOW YOU KNOW HOW TO ADD SHAPES.
The roof width is greater than the cylinder, so we have to modify this dimension using the "scale" block in the "modify" block menu (purple). With this block you can scale the dimensions of a shape in any of the three axis.
NOTE: the axis are represented in the middle of the workplane as color lines: red as the X axis, green as the Y axis and blue as the Z axis. Any value greater than 1, will make the shape bigger in that dimension. Any value between zero and one, will make the shape smaller in that dimension. In this case I am using 0.4 to match the width of the roof, with the diameter of the cylinder. You can just use trial and error to do find this or just use a ratio with the following formula:
Scale ratio in X axis = value in the X axis you want to achieve / value in the X axis you have.
Scale ratio in X axis = 8 (diameter of the cylinder) / 20 (default value of the roof in width) = 0.4 ----Check third image.
NOW YOU KNOW HOW TO SCALE SHAPES.
Now, every shape you add is placed right in the middle of the workplane (in every axis X, Y and Z). We need to use the "rotate" and "move" blocks to position our shape where we want it to be.
NOTE: any modification will only affect the selected shape or group of shapes. If you looked carefully, the roof was the only one affected by the scale block, because the cylinder was deselected once we added the roof. So every rotate or move block will only affect the roof (currently selected).
Let´s modify the roof. 110