Forensic scientists use their knowledge of biology and chemistry to help police solve crimes, but they also need a solid understanding of maths.
What use is maths and why should we learn it?
A forensic scientist could answer that virtually all the mathematics we learn at school is used to solve crimes. Forensic science considers physical evidence relating to criminal activity, and practitioners need competence in maths as well as in the physical, chemical and biological sciences.
Trigonometry, the measurement of triangles, is used in the analysis of blood spatter. The shape indicates the direction the blood has come from. The most probable scenario resulting in blood spatter on walls and floor can be reconstructed using trigonometric analysis. Such analysis can also determine whether the blood originated from a single source or multiple ones.
Suppose a body is found at the foot of a block of flats. Was it an accident, suicide or murder? Using the measured distance from the building together with elementary geometry and dynamics, the forensic scientist can form an opinion as to whether the deceased fell, jumped or was pushed.
Ballistics calculations, such as computing the ricochet angle of a bullet bouncing off a solid surface, use trigonometry. Bullet trajectories determine the distance from shooter to target, and perhaps the height of the gunman and where he was standing when he shot his victim.
The exponential and logarithmic functions, found throughout science, play a key role in forensics. The exponential function relates to processes that depend on the amount of material present as time changes. Rates of heating or cooling, or of the metabolising of alcohol and drugs, are governed by exponential rates of change.
After death, a body cools until it reaches the environmental temperature. By modelling the cooling rate mathematically, using Newton’s law of cooling, an exponential decay of temperature difference is found. This enables estimation of the time elapsed since death. In practice, more elaborate models can be used.
For quantities that vary over many orders of magnitude, such as the concentration of chemicals in the body, the logarithmic function allows us compress them into a more manageable range. The pH scale, which indicates the level of acidity, is of this sort and is often vital in forensic work.