- #1
Mathsig
- 1
- 0
- TL;DR
- 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.
Why Is a Cubic Polynomial Called 'Third Degree'?
- Context: High School
- Thread starter Mathsig
- Start date
-
- Tags
- Cube Cubic Degree Polynomial
Click For Summary
Discussion Overview
The discussion revolves around the terminology used for polynomials, specifically why a third degree polynomial is referred to as a cubic polynomial. Participants explore the connections between the degree of the polynomial and geometric concepts, as well as the naming conventions for other polynomial degrees.
Discussion Character
- Conceptual clarification
Main Points Raised
- One participant questions the connection between the number three and the term "cubic" for third degree polynomials.
- Another participant explains that a cube, being a three-dimensional object, relates to the volume formula ##l^3##, suggesting a link between the term and its geometric meaning.
- A different participant draws a parallel between cubic and quadratic polynomials, noting that the term "quadratic" is derived from the area of a square, which is ##l^2##.
- Further elaboration includes the naming of other polynomial degrees, such as quartic for fourth degree and quintic for fifth degree.
Areas of Agreement / Disagreement
Participants present various explanations for the terminology, but there is no consensus on a singular connection between the terms and their geometric interpretations. The discussion remains open-ended with multiple viewpoints expressed.
Contextual Notes
Some assumptions about the understanding of geometric concepts and terminology may not be explicitly stated, and the discussion does not resolve the underlying reasons for the naming conventions.
- #2
- 29,525
- 21,308
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.
- #3
russ_watters
Mentor
- 23,824
- 11,293
It's the same reason the second degree is square.
- #4
Mark44
Mentor
- 38,089
- 10,638
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).
Similar threads
High School
Finding polynomials with given roots
- · Replies 14 ·
- · Replies 5 ·
- · Replies 1 ·
- · Replies 16 ·
- · Replies 5 ·
- · Replies 9 ·
- · Replies 48 ·
High School
Polynomial degree and root relationship
- · Replies 4 ·
- · Replies 5 ·
- · Replies 4 ·