In the 1680s
the British government
value for the total land area of Britain
prior surveys had produced adequate map
s of the island,
none of these maps had any information on area, and
a new, costly, elaborate survey
teams of surveyors would trace the coastline of the entire island,
and their readings would be combined to produce, after extensive calculation,
a value for the total area.
The astronomer Edmond Halley approached the problem as follows:
- He traced a map of Britain onto thick cardstock.
- He cut out the map's tracing.
- From the remaining cardstock he cut out circles of radius 2 degrees (latitude).
These had an easily calculated area.
- He weighed the cardstock Britain against the circles on a scale.
- The ratio of weight gave, instantly, the ratio of area.
Thus, Edmond Halley solved a difficult and expensive problem for the Queen
simultaneously, invented integration by scissors
as we know it today.
- Halley used this method to calculate the area of a specified shape, as opposed to
the area defined by a specified mathematical function, but the concepts are essentially identical.
- If, as is most likely, Halley worked from a Mercator projection map, the value obtained
is inaccurate, as Mercator maps exaggerate areas increasingly with distance from the equator.
However, Britain is probably limited enough in latitude for his approach to provide a reasonable estimate.