Linear algebra
A dial plate can be laid out, by a pragmatic approach, observing and marking a shadow at regular intervals throughout the day on each day of the year. If the latitude is known the dial plate can be laid out using geometrical construction techniques which rely on projection geometry, or by calculation using the known formulas and trigonometric tables usually using logarithms, or slide rules or more recently computers or mobile phones. Linear algebra has provided a useful language to describe the transformations.