12/19/2023 0 Comments Goldenratio for dummiesIn fact, many people refer to the Golden Ratio as the Greek letter phi. The debate of whether the Egyptians and Greeks, among others, actually used the ratio or whether their products happen to fit into the ratio is still frequently discussed. Egyptians were said to have used this ratio when constructing the Great Pyramids, while the Greeks used it when designing the Parthenon. The Golden Ratio can be found as being included in structures built by Egyptians, and even in the Bible. However, it is also suggested that none of the occurrences of the Golden Ratio were done purposely, but that the structures, paintings, etc. It is suggested that the ratio was discovered and rediscovered many times throughout history. Students will soon find through their explorations that there is not one date that historians can pinpoint as the discovery date of the Golden Ratio. Below is a link for a starter worksheet that could be given to each group to encourage their discussion. Within the group, students should begin discussing the history of the Golden Ratio with one another. Have students form groups of three or four, and allow them to research different mathematicians linked to the Golden Ratio. The Golden Ratio presents a great opportunity for teachers to ignite interest of its history for students. Helping students to explore the mathematicians behind the mathematics may encourage them to become more involved with the learning process. The history behind the mathematics can help students see the topic as more real. One way to do this is to discuss who, what, where, and when the theorems and/or mathematical topics were discovered. I have linked my Geometer's Sketchpad file in which my Golden Ratio tool is included: Golden Ratio Toolīringing mathematics to life is a great way to really get students interested in the topics. The length of segment AC divided by the length of segment AB should give you the value of the Golden Ratio. Mark the intersection point of the circle with the ray.ħ. Draw one more circle centered at the intersection point with the midpoint segment as the radius. Draw a ray starting at the point A and going through the intersection point.Ħ. Mark the point where the circle intersects the perpendicular line. Make a circle using the point B as the center, and the midpoint segment as the radius.ĥ. Create a line perpendicular to the segment at the point B.Ĥ. Create a segment from the midpoint to the point B.ģ. This construction can be used as a demonstration or as an activity for students to explore together as they begin learning about the Golden Ratio.Ģ. Below are the steps to creating your own Golden Ratio using Geometer's Sketchpad. We can also use Geometer's Sketchpad to generate the Golden Ratio. This ratio of one plus the square root of five to the value of two can be created using a pencil, compass, and straight edge. Everything from commercial advertising companies, to painters, to even doctors incorporate this 'magical' ratio into their work.īut what is the Golden Ratio? Mathematically speaking, the value of the Golden Ratio is equivalent to, or about 1.618. The Golden Ratio has been said to be the most appealing ratio, and is therefore used frequently. This ideal ratio is used by many because of its apparent lure of the human eye. The Golden Ratio is a great example of mathematics that we encounter almost daily, without even knowing it. Whether they are able to recognize it or not, mathematics is usually right under their nose. So many students ask the question "When will I ever find or use math in the real world?" I encourage these students to research and explore their every day life for examples of mathematics. Around the World: Finding the Golden Ratio
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