CREATE REGULAR HEXAGON GSP5 SERIES

Therefore, I could determine that the star again weighed less than the circle. From doing this, I found out that the balance scale titled down on the side that the circle was placed. I decided to place the star and a circle on each side. I then did the same by starting to compare the other shapes to the star. I then realized that two stars are equal to the weight of one square. Next, I placed another star on the balance scale and one square. Therefore, I could determine that the square weights more than the star. From doing this, I found that the balance scale titled down on the side that the square was placed. To start, I tried weighting only one star and one square on each side. When playing around with the weight activity, I noticed that some of the objects were heavier than the others. This particular activity investigates the weight value of five objects, a star, a square, a circle, a triangle, and a diamond. The equation below, is the area of the spiral using the square: This will continue to repeat over and over again.Īfter determining what each of the fractions would be for the colored triangles, we then would add up these to get the sum of the area the spiral is covering. Therefore, it would take 16 of the second to largest triangles colored in to cover the entire large square. If we now move to the next triangle colored in, we can determine it would be 1/16 of the original square.

The 1/8 represents that it would take eight of these triangles to cover the entire square. I can see that one of the largest triangles would be 1/8 of the area. That start we need to determine how many of the bigger triangles it would take to cover the entire large square. I am now going to look at the spiral in the square to see how fractions play a part and determine the area. Fractions are hidden within the spiral and we need these fractions to determine how many triangles to color in.

It appears that the spiral can be formed of an infinite number of triangles.

CREATE REGULAR HEXAGON GSP5 SERIES

Thinking more deeply about this, the concept of infinite geometric series can be related to the Baravelle Spiral. Using geometer's sketchpad, I can determine that my triangles are constructed correctly. If the triangles within the regular polygon are constructed correctly, then the base and height of a triangle can be measured and the areas can be then determined with these measurements. The areas of the triangles formed in any Baravelle Spiral form a geometric sequence, starting with the area of the largest triangle, followed by the area of the next largest triangle, and so on. The Baravelle Spirals are closely related to the concept of geometric sequences and series. Part three: How fractions come into play with the Baravelle Spirals Therefore, letting me have more triangles colored in. Also thinking about this more deeply, I could see that the triangles are getting smaller faster in the hexagon than in the square allowing me to then determine that the triangles are taking up less space. However, this spiral in the hexagon will go further because there are more sides in a hexagon than in a square.

This would be the same for the Baravelle Spiral using a square. The only problem is that I can't make the hexagon bigger and bigger in order to show this. Looking at this picture, the spiral would keep going and going. The picture above shows my second Baravelle Spiral using a hexagon. We are done, the spiral curved look will appear. We then repeat this step over and over till Size triangle that touches the first one shaded. In a clockwise direction or a counter-clockwise direction and shade the next Move to the next level of triangles, either Starting triangle that is one of the largest outer triangles and color it. When this is all done, we are actually going to start constructing the Continue doing this for each new polygon itįorms until it becomes too small to work with. Once we have all the midpoints, connect them with straight lines. Once we know what type of regular polygon,įind the midpoints of each side of the polygon. ToĬonstruct a Baravelle Spiral, begin with any regular polygon. It starts to give off the illusion of it being curved. When the pattern is repeated so many times, Pattern that is being repeated over and over again. The spiral is made entirely of straight lines and only appears to look The Baravelle Spiral is a spiral that appears to the humanĮye to be curved, when it actually is not.

Create regular hexagon gsp5