In a dreary backroom of a lonely warehouse, a body lies on the floor. The victim, slightly tilted onto his stomach, is enveloped in a large pool of red blood. Only a few feet away, small splashes of blood stain the dark grey cement wall. Where was the attacker standing when she killed the victim? In real life, crime investigators apply math to solve the fictitious crime scene above. In fact, most forensic science would be nonfunctional without the rigorous application of mathematics. Don’t worry, though, this isn’t like flipping through your regular mathematics textbook (and we won’t take you back to the classroom).

### When will I use this in real life? Angles and triangles

Investigators analyze blood spatter by using trigonometry – the branch of math that measures triangles. For instance, investigators can draw lines from the victim’s body to the blood splashes. They can then measure angles and distances to calculate the third point of the triangle, which is the location of the attacker. From here, they can deduce more information such as how hard the attacker hit the victim.

### Stunning measurements: documenting and assessing

By definition, forensic investigators collect, document and measure. It’s impossible to solve any case without being able to take precise measurements at a murder scene. For example, what if you find foot prints near the victim? You would first need to precisely measure the length to be able to deduce the shoe size. You’d become less suspicious of potential culprits who do not fit this shoe size. A forensic investigator needs to think like a scientist and properly document everything she observes. It involves meticulously measuring not only distance, but weight, temperature and volume to get the numbers right.

### Keeping it proportional: the sum and its parts

When an investigator analyses the gruesome finding of human remains, they’ll apply the math of proportions. Take the finding of a dismembered human arm in a remote part of the woods, for instance. A forensic investigator can measure its weight, length and density to calculate what proportion the arm bone makes up of the victim’s overall height. From there, they can estimate the victim’s height, which would give clues to whether it’s a child or adult, and in some cases, male or female.

### Uncertainty, in principle: it’s not that simple

While we like to think of numbers as being objective, it isn’t always that simple. One example is how DNA gets used as evidence. To compare two samples of DNA, forensic biologists analyze thirteen specific pairs of genes that make up our DNA. These thirteen gene pairs vary tremendously between each of us. In fact, the chance of two people (excluding identical twins, of course) will share the same thirteen pairs is about one in 400 trillion (a number which clearly far exceeds the world’s population). Still, to make a strong identification, what forensic biologists need is a good quality DNA sample.

Despite what any crime-show tells you though, the DNA match is not given with 100% certainty. This is usually because the DNA sample is not ideal: it can be too small, disintegrate over time or become contaminated with other substances. Instead, forensic biologists can ascertain the probability that the DNA is a match. In other words, they can figure out the likelihood that the suspects DNA is the same as the DNA found at the scene of the crime.

Clearly, a forensic investigator needs to rely on more than a magnifying glass and intuition to solve a crime. They must always make sure they get their numbers right: after all, the fate of a defendant’s life can depend on it.

**Your Turn**: Know any more ways that math(s) is used in forensic science? Or are you merely humbled by the sheer usefulness of the subject you once found *so boring*? Let us know in the comments. We’d love to hear from you.

Hello. My name is William Barnedo and I attend South Bay Junior Academy in Torrance, CA. I am a freshman in high school. Recently, my class have chosen a project that deals a lot with forensic science, called Crime Scene Investigators. Our group project will be presented in the Science Fair on March 6. We have to present a crime scene, a police report, and basic information about forensic scientists. I also need to interview a real forensic scientist–so that I can learn how to make a police report, create a crime scene, and get some basic information about forensic science. Would you be willing to help me by having a 5-10 minute interview with me, either by telephone or email? Thank you.

Sincerely,

William Barnedo

P.S

If you do not have time to email me, I would really appreciate it if you referred me to someone. Thanks.

Hi William,

Thanks for your comment. Send us an email at press (at) forensicoutreach (dot) com and someone will get back to you.

How can quadratic, exponential, and sin. functions be applied to forensic science?