The Math of Forensic Science

The Math of Forensic Science Candidate number: 001218-0055 May 2014 Diploma Session

Introduction: Since I was a child, I was always intrigued by the field of forensic science. Watching CSI: Miami and Law & Order: SVU, I was exposed to the wonders of fingerprint identification, blood spatter analysis, and even bullet trajectory. However, back then, it didn’t occur to me the complexity and the relationship that this field had to math. It wasn’t until I began learning the fundamentals of math and the application of mathematics in the real world that I discovered the role math played in this specific field. This exploration will explore the use of mathematics, more specifically trigonometry and calculus in the field of forensic science to give me an in depth understanding of its role in crime scene investigations. Being in my second semester of senior year, I am still uncertain to a certain extent of what major I want to pursue for an undergraduate degree and what career I want to achieve. Having always loved math as its application ceases to amaze me, investigating how it is used in forensic science will help me determine whether or not I want to pursue a degree in forensic science or in criminology. Understanding how what I have learned in math throughout the years can be applied to situations such as forensic science will either make me realize that I want to pursue something math related (forensic science) or not (criminology).

Basics of Blood Spatter Analysis: When forensic scientists are presented with a crime scene that involved blood whether it be a murder, rape or simply a burglary, they must correctly identify the pattern of the blood spatter to accurately determine the source and try and figure out what happened and if the eyewitness testimonies match up with the evidence found. Basically, they need to figure out things like who the perpetrator was, was the person defending themselves, or even when/where the attack was started. All of this of course, depends on the nature of that specific case however, generally, they are looking to determine what happened. They may also use this to determine the height of the victim or the type of weapon used.

Trigonometry to Determine Blood Spatter: Simple trigonometry functions can be used to calculate the impact angle that causes the blood droplet. The impact angle is used to refer to the angle formed when the horizontal axis by an object hitting a plane surface. This can be done by measuring the length and width of the bloodstain and using the simple sine rule. Then, the inverse of the sine rule is found using a

calculator to determine the angle. The length of the bloodstain is used for the hypotenuse and the width is the opposite side of the angle. sine= opposite/hypotenuse The use of mathematics that is used is simply astonishing, as people often wonder when they will ever use math in their daily life or when math is ever useful but in reality, everything has some sort of mathematics fundamental! A new formula has been created to determine the whether or not a victim took a blow standing up or not. This formula helps forensics analysts quickly eliminate possibilities to get closer to the truth in a shorter amount of time. Not only does math help find the source, but it also saves investigators time. This formula takes into account the height of two drops and not only one as the previous technique did. It tells whether or not the blood spatters came from the same source. While analysts may attempt to use logical reasoning to determine this, it is necessary to have valid evidence, hence the use of mathematics. This tells the person’s position whereas the previous example told the where the direction and area the blood came from.

Z0 refers to the height of the blood when it left the body T1 refers to tangent of the angle of first drop hitting the ground T2 refers to tangent of the angle of second drop hitting the ground r2 refers to horizontal distance of the first drop r1 refers to horizontal distance of the second drop The long axis of the blood spatter can be used to determine the area and point of convergence. The point of converge is the area where two blood spatters meet. A line is drawn from the long axis of each blood spatter and the point where they all meet is known as the area of convergence, which is the place where the blood originated from. This is done using something known as the “stringing” method. This allows the analysts to determine where the victim was. There are programs such as HemoSpat and BackTrack that does the math automatically and calculates the angle of impact and all associated math such as the area of origin which uses more complicated

mathematical processes.. An example showing how the area of convergence is found is shown

below. Logarithms and determining when a person deceased: Using Newton’s Principle of Cooling, an equation using logarithms helps forensic scientists in determining when a person was killed or died. The formula is as follows:

t refers to the time T is the temperature measured in oF Rt is the constant room temperature Imaginary Scenerio Police officers were called to a parking lot where they found a dead body. Upon arrival, the coroner checked the temperature of dead person. This was around 10:30 pm. The temperature was found to be 76.5o F. Let’s assume that the room temperature was 60.0o F. The time of death is calculated as follows:

t ≈ 8.5 hours = 8 hours 30 minutes 10:30 pm-8 hours 30 mins = 2:00 pm Approximate time of death: 2:00 p.m This information is then given to police officers or detectives to determine things like if there was something strange about the victims whereabouts at that time of day, or even possibly to rule of suspects who have an alibi for that time.

Conclusion After studying and acknowledging how much math composes forensic science, to me, it seems as if without math this field would not only be difficult, but completely non-existent. It makes me wonder how our ancestors solved crimes without the fundamentals of this subject. Also, to me, forensic science’s backbone is math. Math is what makes us the subject. As seen with the blood spatter, without taking into account where the blood came from or where the person who is the victim was positioned, how would we be able to determine or even rule out possible suspects? Seems impossible to me. Forensic science is a part of law enforcement which is a crucial part of society no matter what country, region, or even continent. However, specifically within the United States, as crime rates are rising, the demand for the use of forensic science is increasing and that means that more work needs to be done in a shorter period of time. Also, since crimes are a very sensitive topic, it is important for scientists to remain as accurate and close as possible to the truth. Using math, forensic scientists are able to more precisely reconstruct a crime scene and determine certain aspects that are vital to solving the crime in a shorter period of time. The

application of mathematics in this field is fascinating but most importantly, it is an extreme necessity.

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