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Mathsig
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- Why is third degree called cubic?
Why is a third degree polynomial called a cubic polynomial? I just don’t see the connection between 3 and a cube.
B Why Is a Cubic Polynomial Called 'Third Degree'?
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- Cube Cubic Degree Polynomial
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A cubic polynomial is called so because it is a third-degree polynomial, analogous to how the volume of a cube is calculated using the formula l^3, where l is the side length. The term "cubic" relates to the three-dimensional nature of a cube, just as "quadratic" refers to the area of a square, which is l^2. The naming convention extends to other polynomial degrees, with quartic for fourth degree and quintic for fifth degree. This terminology reflects the geometric concepts associated with each degree. Understanding these connections clarifies the terminology used in polynomial classification.
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A cube is a three dimensional object. The volume of a cube is ##l^3##, where ##l## is the side length. That's cubic formula, in both senses.
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russ_watters
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It's the same reason the second degree is square.
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Mark44
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Further, a second degree polynomial is called a quadratic polynomial because the area of a square is ##l^2##. The Latin word quadratus means "square."Mathsig said:
Other types of polynomials have names such as quartic (fourth degree) and quintic (fifth degree).
For the sake of argument, lets assume this is, in fact, a right triangle with a rectangle inscribed in it.
Here is what looks like a very elegant solution:
Triangles A and B are similar
a/4=2/b
ab=8
But what is happening in that second line? Is there a property of similar triangles I'm forgetting?
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