slope of slope over time squared

[AntonioLao]

Tangent vector is another name for slope. However, without first defining a coordinate system, both slope and tangent vector could not exist in mathematics. Although the magnitude of the tangent vector is invariance, its directional attribute is coordinate dependent. This dependence suggests that direction is purely an angular measurement in contrast to length and distance or displacement measurement. This angle exists only if it is subtended to one of the axes such that not all of its direction cosines are identically zero. This angular system becomes a Euclidean patch for all n-dimensional curved space-time. However, the slope of space (ordinate) and time (abscissa) is the velocity vector. The slope of velocity (ordinate) and time (abscissa) is the acceleration. A null acceleration is a horizontal line in v-t system while a positive definite constant acceleration is a line subtending an acute angle measured counterclockwise from an axis.

[mkirkpatrick]

Antonio,what exactly are you saying here?You seem to have explained much,but actually
said little!Are you looking for a unifying principle here,that will tie all the loose ends,or what?


regards michael.

[AntonioLao]

Mike,

Math is a very precise field for terms such as slope and tangent vector. The former is defined in high school but the latter is defined in higher abstract math. To me, they are the same.

[mkirkpatrick]

Mike,

Math is a very precise field for terms such as slope and tangent vector. The former is defined in high school but the latter is defined in higher abstract math. To me, they are the same.

Thank you Antonio,I was a little puzzled about that.

regards michael.

[hanzoganz]

Mike,

Math is a very precise field for terms such as slope and tangent vector. The former is defined in high school but the latter is defined in higher abstract math. To me, they are the same.

And as you advance in different areas in maths, you can find lots of other definitions of what a tangent is.

[mkirkpatrick]

And as you advance in different areas in maths, you can find lots of other definitions of what a tangent is.

Thanks for the tip friend,I seem to be going off on a tangent lately,is that the same thing?


regards michael.

[AntonioLao]

I seem to be going off on a tangent lately,is that the same thing?

Tangential motion is needed for continued circular motion.