# This worksheet contains the Maple commands from Chapter 3 of
# Introduction to Scientific Programming by Joseph L. Zachary.
#
# (3.4) This calculates the circumference of the earth in kilometers,
# beginning from Eratosthenes's measurements.
#
> 360 / 7.2 * 5000. * 0.1575;
#
# (3.5) We can save the value of the expression from (3.4) into the
# variable circumference by using an assignment statement.
#
> circumference := 360 / 7.2 * 5000. * 0.1575;
#
# (3.6) Now that we have given circumference a floating-point value, we
# can use it as if it were a floating-point number. We can, for
# example, determine its value.
#
> circumference;
#
# (3.7) We can also use its value in more complicated expressions.
#
> diameter := circumference / 3.14159;
#
# (3.8) Here we recompute circumference using parentheses to explicitly
# group the operands and operators from (3.5).
#
> circumference := (360 / 7.2) * (5000. * 0.1575);
#
# (3.9) The Digits variable is consulted by Maple to determine how many
# digits to use in the mantissas of floating-point numbers. Its value
# can be modified via assignment.
#
> Digits := 4;
#
# (3.10) Now when we repeat the calculation from (3.5), we obtain a
# four-digit result. (Maple adds the trailing zero so that the
# magnitude of the result will be correct.)
#
> four_digit_circum := 360 / 7.2 * 5000. * 0.1575;
#
# (3.11) We can also obtain a four-digit approximation to the earth's
# diameter.
#
> four_digit_diameter := four_digit_circum / 3.1;
#
# Let's set the mantissa size back to ten.
#
> Digits := 10;
#
# (3.12) This is part of an interval arithmetic computation. We use
# the smallest possible value (7.15) for the angle measured by
# Eratosthenes, the largest possible value (5050) for the distance from
# Alexandria to Cyrene, and the largest possible value for the
# conversion factor from stadia to kilometers. This gives us the
# largest possible value for the circumference of the earth.
#
> (360 / 7.15) * 5050. * 0.15755;
#
# (3.13) We compute the smallest possible value for the circumference
# of the earth by perturbing the measurements in the other direction.
#
> (360 / 7.25) * 4950. * 0.15745;
>