Our goal is to solve for X. Intuitively you could say that since 5 is half way between 4 and 6, X must be half way between 3 and 5. So it’s 4, and that’s basically how it works.
The mathematical process is to set the ratio of the differences equal to each other.
The ratio of the differences in one row in the table is set equal to the ratio of the differences in another row.
Solve for X, and it’s equal to 4.
So interpolation uses the ratio of differences of values in the table to find values not found in the table. It finds the value between known values.
Extrapolation uses the same process, except it finds values outside known values. The table only goes to 10 mm radii, so you could use extrapolation to find the value for an 11 mm radius. You just need to image having an 11 mm column, and use the same process.
These are examples of interpolation and extrapolation between columns. You can use the same procedure between rows, and between tables.
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