Numerical Stability
Heron's formula as given above is numerically unstable for triangles with a very small angle. A stable alternative involves arranging the lengths of the sides so that and computing
The brackets in the above formula are required in order to prevent numerical instability in the evaluation.
Read more about this topic: Heron's Formula
Famous quotes containing the words numerical and/or stability:
“The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)
“Free from public debt, at peace with all the world, and with no complicated interests to consult in our intercourse with foreign powers, the present may be hailed as the epoch in our history the most favorable for the settlement of those principles in our domestic policy which shall be best calculated to give stability to our Republic and secure the blessings of freedom to our citizens.”
—Andrew Jackson (1767–1845)