More Math in Forensics.

  Since I've spent quite a bit of time watching Forensic Files during my visit to Hawaii, I wondered what other math they use in Forensics beside blood splatter and height based on shadows.

In general terms, crime scene technicians must use precise measurements so they can eliminate those.  For instance, if they know the length of the shoe print, they know the size of the perpetrator based on the length of the shoe.  I recently ordered a pair of shoes from a company who requested I measure my foot in centimeters so I could order the correct size.

In addition, proportions are frequently used in forensics to provide additional information.  An example would be if a human leg bone were found, they could then use mathematical equations to figure out what proportion of a person's height is before calculating the actual height. They can also determine if the person was a child or adult.  Furthermore, they can use the length of a person's stride to help determine their height.

Forensic scientists often state their results in probabilities such as the DNA sample matched the DNA found at the scene so the chance of the person doing it was 1 in 2 billion people.  This provides juries with a better idea of how accurate the match is.

Specific examples using mathematics in forensic scientists vary.  One way is to use the ratio of the diameter of the medulla or center pigmented part of the hair to the diameter of the whole hair strand. 
If the ratio is less than .5, the hair is human.  If its greater than .5, the hair is animal. In addition, by careful examination, it is possible to determine the type of animal the hair is from.

To determine if the pelvic region of a skeleton comes from a male or female, examiners check the angle between the inferior public rami or the angle in the front between the two halves.  If the angle is an acute angle of about 70 degrees, but women have an obtuse angle of 90 to 100 degrees.  Forensic scientists often use a protractor to determine the angle.

When comparing fingerprints, they look at distances between grooves, and certain obvious patterns.  Distance indicates measurements because the anomalies must be exactly the same distance on both prints or they may not be considered a match.

Lie detector interpretation relies on blood pressure, pulse rate, and breathing while the length of a skid mark plugged into a formula can determine the speed of the vehicle.  This one I know about.  A family member was sited for speeding after hitting a street sweeper that was performing a U-turn just past a blind curve.  We went and measured the length of the skid marks, I looked up the formula so I could check their calculations. They were wrong in their calculations.  I proved he was not going more than 37.5mph in a 35 mph zone. They came back and charged him with negligent driving but at the trial,  the ticket was thrown out due to being totally prepared mathematically and scientifically.

There is so much more they can determine based on the evidence and through the use of mathematics.  This is just a bit of the math used by forensic scientists.