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Using Mathematics to Solve Crime

Typically, when people ask me why I want to go into Law Enforcement, I shut down. It’s a simple question, really, but the answer isn’t so straightforward. But this essay is living proof that I want to solve crimes; this is proof that I desire to become a sleuth like Nancy Drew. Definitely. Of course, one would only assume that a simple statement like that would be the beginning of a fifth-grade story for Language Arts. But this is nothing of the kind, in fact, this is the work of a college student conveying her aspirations in the form of an essay. The purpose of this essay it to draw a connection between math and sleuthing; I am going to find a correlation between mathematics and criminal justice. According to an interview (conducted by Pamme Boutselis) Police Officer Tim McMillan—Bachelor of Arts in Mathematics— gives us a glimpse of why he does what he does and how math applies to it. When he was almost 21 years old, a couple of his friends were murdered in a home invasion. He recalls that the suspect was caught and prosecuted, but all the culprit took was a DVD from the home. “I had never experienced tragedy, and — being so young — it really, really bothered me. Very shortly after that, I enrolled in the police academy and have been working as an officer ever since (McMillan, 2015).”  Many people end up in the police force in the aftermath of a tragedy similar to this one. I, on the other hand, cannot relate to any such scenario, but I do have a passion to make the world a better place; a vendetta, if you will. Now, the average person probably knows that the field of law enforcement deals heavily with ballistics, forensic analysis, and chemistry. But, what the average person does not know is that not only does Law Enforcement deal with science, but math as well. According to McMillan, “one of the most successful data-driven solutions I’ve seen in other agencies is the employment of data analysts who examine crime waves and deploy their assets to certain geographical locations based on what the crime stats are telling them. You’re almost trying to predict the future by using mathematics and analyzing past events (2015).” He asserts that mathematics has given way to a huge influx of data and information. “We’re in the computer age, where we can extract data in seconds (2015).” Now, when McMillan started off in college, he was originally shooting for a degree in Criminal Justice (at this point, he had been on the police force for ten years). He decided he didn’t think a degree in Criminal Justice would be worth it, considering he knew all he needed to know—academically—in that area. So, he changed his major to a BA in Mathematics. “Data analysis applied statistics and applied mathematics are being used throughout the country and progressively in law enforcement agencies, and I wanted to be on the forefront (2015).” He gives us an example of how math applies to his job on the Police Force. He had an ongoing occurrence of cars being stolen from gas stations—where the keys are left dangling from the ignition and a perpetrator hops in a flees. So, they set up a hot seat: a bait car. The bait car was jimmied so that the perpetrator could hop in the car and drive away, but the Police Force had a remote control to shut the car down and lock the perpetrator from the inside. “I was able to do the time analysis beforehand using applied mathematics — the same procedure that’s in any other statistical research — to determine what times were the best times to do this operation. We didn’t have to go out there randomly last night. We were able to have a plan as to what time statistically tipped the scales in our favor (McMillan, 2015).” During the time McMillan spent in college, his eyes were opened as he saw all the ways math coincided with Law Enforcement, things like the scenario with the car. Who would think math really does apply to Solving Crimes? (Mathematics Applied: Modern Applications of Math in Law Enforcement, 2015) Math is a huge break-through for the field of Criminal Justice; it proves theories and solves crimes through the use of equations and step-by-step analytics.

Modern Applications of Math in Solving Crimes

In, The Numbers Behind NUMB3RS: Solving Crime with Mathematics— by Keith Devlin and Gary Lorden– the crime-acclimated television show, NUMB3RS, is dissected to prove how math is the secret weapon to solving enigmas. In the show, one of the protagonists is a mathematician, and much of the action revolves around him. Professor Charlie Eppes uses his crazy math services to help his older brother—FBI Agent Don Eppes— identify and prosecute criminals. Although the show is produced by Paramount Network Television and has received high ratings, many viewers deem the story line as implausible: math can’t solve crimes. However, as I already proved, you can. Law Enforcement Agencies and Police Forces use math in every instance they can.  The purpose of this book, as the authors describe, is to show society some of the math techniques that the Police Force, the FBI, and the CIA frequently use. “Most of these methods have been mentioned during episodes of NUMB3RS” (Devlin and Lorden 2007). Among these methods are data mining. Tools used in data mining are: Link analysis —looking for associations and other forms of connection among, say, criminals or terrorists, Geometric clustering —a specific form of link analysis, Software agents —small, self-contained pieces of computer code that can monitor, retrieve, analyze, and act on information, Machine learning —algorithms that can extract profiles of criminals and graphical maps of crimes, and Neural networks —special kinds of computer programs that can predict the probability of crimes and terrorist attacks (Devlin and Lorden 2007).

Modern Applications of Math in Crime Scene Investigations

One of the reasons why we have learned math (practically our whole lives), but especially in college, is to develop keen thinking and problem-solving skills.  Now, as a police officer or an investigator in law enforcement, problems will find you like food finds its way to a grocery store. Now, are all those problems going to involve mathematics? No, but because you (hopefully) payed attention in math from grades k-12, your brain developed keen awareness, which is what police officers use daily. So, for the problems that do, indeed, involve math, geometry may help you as a police officer. For example, lets’ say there was a car accident, and you’re the deputy in charge of the scene. You need to be able to determine where car a was coming from when it car b. Also, say you get a call that someone was shot, and you arrive at the scene and find everything in disarray. It would be useful to determine where the victim was standing when he/or she was shot/or stabbed—this is called ballistics in the case that someone was shot (Geometry for Police Officers, 1997).

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There are many sectors in ‘solving crimes’, however, a big sector comes from the crime scene. A great example applying math to a crime scene is through the analysis of blood spatter. Blood accounts for 8% of your total body weight, 5 to 6 liters of blood for males, 4 to 5 liters for females. A 40% blood volume loss (internally and/or externally) is required to produce irreversible shock (death). Blood loss of 1.5 liters (internally or externally) is needed to cause the loss of consciousness. The three categories of bloodstains are Passive, Projected, and Transfer.

Blood spatter evidence in American legal cases did not occur until 1955, when Dr. Paul Kirk submitted his findings in well renown case. The field saw a modernization break-through in the work of innovative forensic scientist Herbert MacDonell. MacDonell trained law-enforcement personnel in blood spatter analysis and developed courses to continue to train analysts. In 1983, he and other attendees of the first Advanced Bloodstain Institute founded the International Association of Bloodstain Pattern Analysts (IABPA). Prior to the 1970s, blood analysis used a system of categories based on the velocity of blood drops at impact: Low-velocity impact spatters (LVIS) that resulted from dripping and were assisted by gravity alone, Medium-velocity impact spatters (MVIS), which were slower than those produced by a gunshot but faster than gravity drips and High-velocity impact spatters (HVIS), produced by gunshots or fast-moving machinery. After the 1970s, these definitions changed. Instead of “impact” referring to the speed of the droplets, it came to refer to the speed of the weapon or object that sent them flying. These new interpretations gave way too many unknown factors. Also, they lead investigators to make assumptions based on outside information — for example, to assume that droplets were HVIS because the case involved a suspected shooting. To deter this, analysts today use more specific terms. LVIS, for example, might be called “gravitational drops” or “drips”.  Investigators use calipers to measure the blood drop (length and width). Then, by using the Law of Sine, they find the angle of impact of the blood drop, and later calculate the height of the source of blood using the law of tangents. Furthermore, hairs are often discovered at crime scenes, however, only using math can determine whether it is a human or an animal hair. You can do so by calculating the ratio of the diameter of the medulla (middle, pigmented section of the hair) to the diameter of the entire hair. An animal hair parades a ratio of ≤.5, while a human hair parades a ration of ≥.5.

Criminal Justice needs Math

The New Mathways Project, a collaboration of The Charles A. Dana Center at The University of Texas at Austin and the Texas Association of Community Colleges, writes a compelling article about high-demand fields recruiting students with college degrees in C.J. in the state of Texas. In Texas, 2012, 3,365 students had a degree in C.J. Now, with that in mind, there are many mathematicians out there who are suggesting colleges should “offer multiple mathematics pathways with relevant and challenging math content aligned to specific programs of study” (Cullinane and Tow). The Academy of Criminal Justice Sciences states that the “primary objectives of all criminal justice programs include the development of critical thinking; communication, technology and computing skills; quantitative reasoning; ethical decision-making; and an understanding of diversity” (ACJS, 2005, p. 10). ACJS endorses statistics as a must for students in line to receive a C.J. degree (ACJS, 2005, p. 9). According to the Mathematical Association of America, “students in social science majors require a strong foundation in mathematical literacy—particularly in the area of statistics in order to succeed in a data-driven career field” (Johnson and Grant, 2011, p. 34). The Texas Higher Education recommends 3-hour credit of a math class (THECB, n. d., table). Criminal Justice needs to keep using math like cookies need chocolate chips. There are other ingredients to put in cookies, but chocolate chip cookies were the original cookie and therefore cannot be replaced. Math cannot be replaced, it is original. You can use other methods to find solutions, but at the end of the day, math is the only thing that works.


            More and more students receiving higher education and aiming to achieve a C.J. Degree are also getting Math Degrees as well. Why is that? Math is applicable to Criminal Justice in the same way butter is lathered on bread. As in the crime scene examples, only math could be used to distinguish between an animal hair and a human hair; that could determine if someone was at the crime scene or not—a human hair sample could lead investigators to a potential suspect, otherwise unknown. Talk about tying up loose ends, I think math could do that, too.


  • Academy of Criminal Justice Sciences. Certification Standards for College/University Criminal Justice Baccalaureate Degree Programs, p.10. Retrieved from ACJSCertificationStandards-Baccalaureate.pdf
  • Bertino, Anthony & Patricia, Nolan. Examples of Math Applications in Forensic Investigations.
  • Cullinane, Jesse & Tow, Jenna. Mathematics for Criminal Justice. Retrieved from
  • Geometry for Police Officers. (n.d.). Retrieved from
  • Johnson, J. A., & Grant, P. H. (2011). “Social Science: CRAFTY Curriculum Foundations II Project.” Page 34 in Ganter, S. L., & Haver, W. E., editors. Partner Discipline Recommendations for Introductory College Mathematics and the Implications for College Algebra, Washington, DC: Mathematical Association of America.
  • Mathematics Applied: Modern Applications of Math in Law Enforcement. (n.d.). Retrieved from
  • Texas Higher Education Coordinating Board. (n.d.). Field of Study Curriculum for Criminal Justice. Retrieved from
  • Texas Higher Education Coordinating Board Data. (2014). Degrees Awarded by Award Level / Curriculum Area 2012-2013 [Database]. Retrieved from


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