10/26/2022 0 Comments Create regular hexagon gsp5If N is bigger than 6, we obtain a polygon with a hole in the middle. Here's how it looks:įor N = 6 and X = Z = 1, we obtain the exact same hexagon as in the classic method, without using any additional lists! After changing the value of N, we can obtain different polygons, for instance a pentagon: Now, to calculate the positions of the remaining pieces, we can subtract A from the position of the original object and then add A rotated by a certain angle. Here we use the fact that cotangent of an angle is equal to its cosine divided by its sine: Its X and Y coordinates are both equal to 0, while the Z coordinate can be computed using trigonometry: Now we need to calculate the vector from the origin of our polygon to the origin of our square object. Variable N is the number of sides of our polygon, while X and Z denote the size of our original square object. Using this method, we can also create regular polygons with different number of sides! Instead of creating the list of positions, they can be calculated in Fancade using trigonometric functions. Here we go! A perfect regular hexagon! Advanced method See what happened to our original object! We also need to rotate them (by 60°, 120° etc) and for that, we're going to use the Make Rotation block. We create the remaining pieces and we set their positions using the list above. Now our hexagon can be created with a simple loop. Let's put them in a list (starting from index 1 for convenience): Construct a non-regular hexagon ABCDEF (something like the one below) so that sides AB and ED are parallel and congruent. These coordinates are not exact (the exact coordinates are irrational and they require a square root of three), but three decimal places is enough for our hexagon to look good. To obtain the coordinates of the remaining pieces, we need to add the following vectors to the position of the original piece: This piece will be copied 5 times and the other pieces will be placed relative to the original one. We're going to create a green hexagon with a darker boundary, so our piece looks like this: First of all, we need to create a square piece. Hexagons are made out of 6 square pieces, properly placed, and rotated. This exact method is used to create hexagons in games Hexoban and Hexals. Create regular hexagon gsp5 how to#Q3 Do you think a regular heptagon (seven sides) would tessellate? Explain.This is a tutorial on how to create a perfect regular hexagon in Fancade. Q2 Which of the regular polygons you tried will tessellate and which won’t? Why? Answer on a separate sheet. Repeat the investigation with squares, regular pentagons, regular hexagons, and regular octagons. Why do equilateral triangles work? (Hint: It has to do with their angles.) 6. You can tile the plane with them without gaps or overlapping. Q1 So far, you’ve demonstrated that equilateral triangles can tessellate. Keep attaching triangles to edges of existing triangles until you have triangles completely surrounding at least two points. Drag several points on the triangles to make sure they’re really attached. Use the custom tool again, this time clicking in the opposite direction, to construct a second equilateral triangle attached to the first. Pay attention to the direction in which the triangle is created as you use the tool. On a blank page, or in a blank sketch, use a custom tool to construct an equilateral triangle. Open the sketch Islamic_Tessellations.gsp if it is not already opened. Such custom tools come with the sketch below, but you may want to create them yourself. Each custom tool must create its figure from the endpoints of one side of the polygon-not from the center. You’ll need custom tools for creating equilateral triangles, squares, regular pentagons, regular hexagons, and regular octagons. Are there other shapes that would make good tiles? In this investigation, you’ll discover which regular polygons tessellate. This kind of tiling is sometimes called a tessellation. Squares make good tiles because they can cover a surface without any gaps or overlapping. Tessellating with Regular Polygons Name(s): You’ve probably seen a floor tiled with square tiles. You must always start and end your dragging with the cursor positioned on an existing point. If your triangles don’t stay attached, undo until the second triangle goes away, then try again. Click twice in the sketch to use the tool. Click on the Custom tools icon (the bottom tool in the Toolbox) and choose the desired tool from the menu that appears.
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