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.

Forensics.

  As you know, I find the math in forensics quite interesting.  It is a way of finding information from the evidence to find the perpetrator.

On all those shows, they find the guilty person within one hour, well 45 minutes give or take a couple minutes.

In reality it can take up to a year or longer.  There was a murder in the village I live in.  A young lady was stabbed multiple times and left behind the clinic.  The police came out, interviewed everyone, gathered data, found evidence, and took forever but almost a year later, they arrested a young man for the crime. I shared one way I'd used math to prove a person not guilty of reckless driving.

Lets look at some other ways math is used in forensics to help solve crimes.

1.  One can tell an animal hair from a human hair by calculating the ratio of the diameter of medulla to the diameter of the whole hair.  If it is .5 or higher, it is animal hair.  If it is lower than .5, it is human hair.

2. Estimating the size of an individual grain of pollen using the magnification of a microscope.  The idea is to estimate how many grains of pollen will fit across and divide the size of the field of view by that and voila, you have the individual size.

3. Blood splatter uses trigonometric calculations using the height and distance to find the angle of impact.  height is opposite while distance to the splatter is adjacent.

4. Using angles, they can tell if the pelvic bones are from a male or female.  If the angle beneath the ischia bones is less than 90 degrees (forms an acute angle), it is male.  If it is greater than 90 degrees ( forms an obtuse angle), its a female. 

5. Time of death, looking at the drop in the body temperature.  For the first 12 hours, the body cools by 1.4 degrees F each hour.  After 12 hours, heat loss is calculated at .7 degrees F each hour.

6. Time of death based on insect development.  They can use the development of certain insects to approximate a time of death because insects require a certain temperature to hatch and progress from one stage to another.

If the math is packaged in something as exciting as helping to solve a crime, students are more willing to do the calculations because it is a fun and applicable situation.  I'll give some sites for creating a unit next week. 

Let me know what you think.