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README.md, README.tex.md: Fix typo (s/therefor/therefore/) #51

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4 changes: 2 additions & 2 deletions README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -71,7 +71,7 @@ another point on the curve <img src="./tex/bb6c9ad7258cdd805398547a25e53aac.svg?
It always possible, and often convenient, to assume without loss of generality
that <img src="./tex/6f9bad7347b91ceebebd3ad7e6f6f2d1.svg?invert_in_darkmode" align=middle width=7.7054801999999905pt height=14.15524440000002pt/> is an [arc length
parameterization](https://en.wikipedia.org/wiki/Arc_length) of the curve <img src="./tex/193089f7a231633473714830d2edc62a.svg?invert_in_darkmode" align=middle width=9.423880949999988pt height=14.15524440000002pt/> so
that <img src="./tex/41298c93d4b1388e9d8cf7017938b420.svg?invert_in_darkmode" align=middle width=60.61099604999999pt height=24.7161288pt/> and therefor the unit tangent vector is simply <img src="./tex/5f8e197a7e88cc7cd47d4ed2a8f3ebd4.svg?invert_in_darkmode" align=middle width=84.28675199999999pt height=24.7161288pt/>.
that <img src="./tex/41298c93d4b1388e9d8cf7017938b420.svg?invert_in_darkmode" align=middle width=60.61099604999999pt height=24.7161288pt/> and therefore the unit tangent vector is simply <img src="./tex/5f8e197a7e88cc7cd47d4ed2a8f3ebd4.svg?invert_in_darkmode" align=middle width=84.28675199999999pt height=24.7161288pt/>.

In an analogous fashion, we can consider the limit of the
[circumcircle](https://en.wikipedia.org/wiki/Circumscribed_circle)
Expand Down Expand Up @@ -191,7 +191,7 @@ loops, etc.

In the discrete world, if a curve is represented as a piecewise-linear chain of
segments, then it's natural to associate curvature with vertices: the segments
are flat and therefor contain no curvature.
are flat and therefore contain no curvature.

A natural analog to the definition of curvature as
the derivative of the tangent vector
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4 changes: 2 additions & 2 deletions README.tex.md
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Expand Up @@ -74,7 +74,7 @@ $$
It always possible, and often convenient, to assume without loss of generality
that $s$ is an [arc length
parameterization](https://en.wikipedia.org/wiki/Arc_length) of the curve ${\gamma}$ so
that $\|{\gamma}'\| = 1$ and therefor the unit tangent vector is simply $\mathbf{t}(s) =
that $\|{\gamma}'\| = 1$ and therefore the unit tangent vector is simply $\mathbf{t}(s) =
{\gamma}'(s)$.

In an analogous fashion, we can consider the limit of the
Expand Down Expand Up @@ -215,7 +215,7 @@ loops, etc.

In the discrete world, if a curve is represented as a piecewise-linear chain of
segments, then it's natural to associate curvature with vertices: the segments
are flat and therefor contain no curvature.
are flat and therefore contain no curvature.

A natural analog to the definition of curvature as
the derivative of the tangent vector
Expand Down