Compute barycentric coordinates of a tetrahedron

$$\begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} \mathbf P_1 - \mathbf P_4 & \mathbf P_2 - \mathbf P_4 & \mathbf P_3 - \mathbf P_4 \end{bmatrix}^{-1} .  \begin{bmatrix} \mathbf P - \mathbf P_4 \end{bmatrix} \\
d = 1 - a - b - c - d
$$

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√4 + 40 = ?

The Least Perceptive Literary Critic
The most important critic in our field of study is Lord Halifax. A
most individual judge of poetry, he once invited Alexander Pope round to
give a public reading of his latest poem.
Pope, the leading poet of his day, was greatly surprised when Lord
Halifax stopped him four or five times and said, "I beg your pardon, Mr.
Pope, but there is something in that passage that does not quite please me."
Pope was rendered speechless, as this fine critic suggested sizeable
and unwise emendations to his latest masterpiece. "Be so good as to mark
the place and consider at your leisure. I'm sure you can give it a better
turn."
After the reading, a good friend of Lord Halifax, a certain Dr.
Garth, took the stunned Pope to one side. "There is no need to touch the
lines," he said. "All you need do is leave them just as they are, call on
Lord Halifax two or three months hence, thank him for his kind observation
on those passages, and then read them to him as altered. I have known him
much longer than you have, and will be answerable for the event."
Pope took his advice, called on Lord Halifax and read the poem
exactly as it was before. His unique critical faculties had lost none of
their edge. "Ay", he commented, "now they are perfectly right. Nothing can
be better."
-- Stephen Pile, "The Book of Heroic Failures"