From e5f44d97c6652f262c82b5c796c07a7a22a00e90 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 4 Jul 2021 20:02:27 +0200
Subject: Expand knowledge base

---
 content/know/concept/legendre-transform/index.pdc | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

(limited to 'content/know/concept/legendre-transform/index.pdc')

diff --git a/content/know/concept/legendre-transform/index.pdc b/content/know/concept/legendre-transform/index.pdc
index 290a89a..9cb6824 100644
--- a/content/know/concept/legendre-transform/index.pdc
+++ b/content/know/concept/legendre-transform/index.pdc
@@ -27,9 +27,9 @@ $$\begin{aligned}
     y(x) = f'(x_0) (x - x_0) + f(x_0) = f'(x_0) x - C
 \end{aligned}$$
 
-The Legendre transform $L(f')$ is defined such that $L(f'(x_0)) = C$ (or
-sometimes $-C$ instead) for all $x_0 \in [a, b]$, where $C$ is the
-constant corresponding to the tangent line at $x = x_0$. This yields:
+The Legendre transform $L(f')$ is defined such that $L(f'(x_0)) = C$
+(or sometimes $-C$) for all $x_0 \in [a, b]$,
+where $C$ corresponds to the tangent line at $x = x_0$. This yields:
 
 $$\begin{aligned}
     L(f'(x)) = f'(x) \: x - f(x)
@@ -85,7 +85,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Legendre transformation is important in physics,
-since it connects Lagrangian and Hamiltonian mechanics to each other.
+since it connects [Lagrangian](/know/concept/lagrangian-mechanics/)
+and Hamiltonian mechanics to each other.
 It is also used to convert between thermodynamic potentials.
 
 
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