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todd098
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I am having trouble finding the relationship between a 72-72-36 triangle and the golden ratio. Could someone point me in the right direction or explain it? Thanks
todd098 said:I am having trouble finding the relationship between a 72-72-36 triangle and the golden ratio. Could someone point me in the right direction or explain it? Thanks
The golden ratio, also known as the divine proportion or phi, is a mathematical concept that is represented by the Greek letter phi (φ). It is approximately equal to 1.618 and is believed to be aesthetically pleasing.
The golden ratio is closely related to triangles, particularly equilateral triangles. If you draw an arc from the midpoint of one side of an equilateral triangle to the opposite vertex, the length of that arc will be exactly half of the length of the side of the triangle. This creates a smaller equilateral triangle within the original one, and the ratio of the larger triangle to the smaller one is equal to the golden ratio.
The golden ratio is considered to be a fundamental building block in geometry. It can be found in many natural phenomena, including the proportions of the human body, the growth patterns of plants, and the structure of galaxies. It also has practical applications in architecture, art, and design.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Interestingly, if the length of one of the shorter sides is divided by the longer side, the result is approximately equal to the golden ratio.
The golden triangle is a special type of isosceles triangle where the ratio of the length of the base to the length of the other two sides is equal to the golden ratio. This creates a unique shape that is believed to have aesthetic appeal. The golden ratio is also used in the construction of the golden spiral, which is formed by connecting smaller golden triangles within a larger one.