logan3 said:What would be the point of knowing information about the subtangent and subnormal lines? Do they have any worthwhile real-world applications? Wikipedia says that they are archaic and fell into disuse after the early 20th century.
Thank-you
Subtangent and subnormal lines are two types of lines that are used in calculus to approximate the slope and curvature of a curve at a given point.
The subtangent is calculated by drawing a tangent line at the given point on the curve and then drawing a line perpendicular to it that intersects the x-axis. The subnormal is calculated by drawing a line perpendicular to the tangent line that intersects the y-axis.
Subtangent and subnormal lines help us to approximate the slope and curvature of a curve at a given point, which is important in understanding the behavior of functions and solving real-world problems in various fields such as physics, engineering, and economics.
No, subtangent and subnormal lines are only approximations of the actual slope and curvature of a curve at a given point. The accuracy of these lines depends on the smoothness of the curve and the distance of the point from the curve's inflection points.
Yes, subtangent and subnormal lines can be used for any type of curve, as long as the curve is differentiable at the given point. However, for more complex curves, other methods may be needed to accurately estimate the slope and curvature.