Creating Shapes with Robots
With the triangle. I first thought of the angles that would need to be met. I know that a triangle has a total of 180 degrees when all of the angles are added. So I initial thought "ya it needs to turn 30 degrees for each corner: WRONG. That's the angle measurement from within the triangle. And I know that measuring the angles outside of a shape, that they will all add to 360. 360 divided by 3 is 120. 120 is the angle that needed to be met when making an acute triangle for each turn. Got it first try.
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The pentagon wasn't too much harder, it was the same concept and rule when looking for angles of rotation. yet again we are measuring from the outside so all of the angles will add to 360. And we have 5 points that we need to rotate at to complete the shape. 360 divided by 5 is 72. 72 was the angle that needed to be turned when making the pentagon. Just like the triangle, I got this on my first attempt. Now it's important to note that this is only applicable in the aspect of symmetrical shapes. At least when it comes to the pattern of travelling a fixed distance and rotating a fixed angle for how ever many sides a shape has. That is the basic rule for drawing a symmetrical shape.
Now this was a bit more tricky because we are introducing two angles that need to be met for making this shape; a six sided star. Most of my peers decided to go with drawing in a circular motion; so turning 45 degrees, then 120, 45, then 120. I found this to be tedious and overly complicated. So I used a method that involved around 3 or 4 steps. Because I noticed that it is composed of two acute triangles and all I would simply need to do is draw out one triangle, go forward on unit, turn 45 degrees and draw another acute triangle. Which gave me this almost perfect star of David. I say almost because with every single shape I drew, the traction of the wheels and baring was never perfect. This took me 3 tries to get this final product.
It's a little hard to see but this is a 5 pointed star. And this was by far the hardest challenge yet. Oddly enough my friends and peers decided to draw it out with a pattern of angles and distances going all the way around like a circle. But this was way too much work and there is a much more simple solution. If you've ever drawing out a star on a piece of paper, more than likely you've drawn out the kind where the lines intersect through the middle making a pentagon. This is easier because unlike tracing it out from the outside only, There is only one angle that needs to be repeated and that is 145 degrees. And you're only turning in one direction as apposed to tracing it from the out side you are turning left and right using two different angles. I got this on my very first try and on the right is how it came out.
Now we are met with the final boss; the house. The reason this was so difficult is because we need to use Pythagorean theorem to find the two lines that make an X in the center of the house as you can see. And on top of the, the lines were not allowed to intersect. So I began with the bottom and worked up the house from there. First I traveled a distance of 2, rotated 90 degrees and up two. Now it's time for the hard part. I know since it's a right triangle we need to cut directly in between the square in a diagonal line meeting the other corner. 90 degrees would continue the square, while half of that (45 degrees) would cut it. Now we need to find the hypotenuse which is the longest side of a right triangle which in this case is what we are drawing. Both sides squared, add them, and then find the square root of that sum. it came out at about 1.4, so now we have our side length. From here it's pretty straight forward, we go up two, then make an acute triangle up top like we have done before. And the final step is to rotate 45 degrees the opposite way and travel 1.4. We have made a house with out going over any line twice. This took 5 tries! But it was worth it to see all of it come together in the end.
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