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Mathematics and Forensic Science

The many crimes that occur today, such as theft mayhem, and murder makes it necessary to find the perpetrators to be punished according to the law. By relying on the examination of various evidence with scientific knowledge and technology to find evidence confirming the guilt of those people. This creates a demand for forensics specialists. And a new field was born, namely Forensic Science, which will focus on applying the knowledge of mathematics, physics, chemistry, biology, entomology and technology to be applied in the investigation of various cases.

One proposed method of forensic science is to use mathematical knowledge to determine the location of an injured victim from the distribution of blood droplets and to explain what happened at the crime scene. The blood trace assumed the events in the room where the murder occurred and predicted where the victim was attacked in the room. Is there a fight? Or was there a fight at the scene or not? Or is it a scene to disguise the case? By using the knowledge of trigonometry learned in grade 5

First consider spherical droplets of blood moving in the air. It hits any surface, be it a floor, wall or ceiling, if this drop of blood moves perpendicular to the surface. The blood will spread evenly in all directions. And will get a blood that looks like a circle. So what will happen? If the drop of blood moves at an angle of less than 90 0 to the surface

in fact When a murder case Blood often comes out of the victim’s body. and then bounce off different surfaces with this movement at an angle to the surface If a drop of blood moves at an angle q less than 90 0 (0 < q < 90 0 ), when the drop of blood hits the surface, the blood spreads and elongates in the direction of movement.

The bloodstain is oval-shaped as in Figure 1. When W is the width of the bloodstain and L is the length of the bloodstain as in Figure 2, it can be seen that the width of the bloodstain is equal to the length of the diameter of the droplet. blood At this point, the reader may wonder why the width of the bloodstain is equal to the length of the diameter of the blood drop.

If the trajectory of the blood drop is compared to a cylindrical tube with an elliptical cross-section at the end of the tube, as in Figure 3, it can be seen that the length of the diameter of the blood drop is equal to the width of the ellipse, and from Figure 1 we can find The magnitude of the angle of the path of the blood drop to the ground when the width and length of the blood mark are known, where q is the size of the angle of the path of the blood drop to the ground, we get …

Consider the drop of blood moving from the victim. When the blood hits the ground by the gravity of the earth while the victim is moving, a horizontal force is created. Therefore, when the blood hits the ground, Therefore, the angle that the trajectory of the blood drop to the ground is not 90 0 as in Figure 4.

This equation can be used to calculate the speed of movement of the injured person. From the measurement of the angle at which the blood hits the ground, the magnitude of the vertical velocity, represented by V y , is calculated using the height from the ground to the point of origin of the blood, such as the head, arm, torso or leg.

where h is the height from the ground to the origin of blood and g is the acceleration due to Earth’s gravity. (assuming air resistance does not have a significant effect This is true for large drops of blood that travel down a short distance.)

Examples of applying forensic science knowledge to find facts for use in investigations such as

The distribution pattern of the bloodstain is determined by the impact of a large number of blood droplets on the surface. This often occurs simultaneously from the same blood source, such as a blow to the head or a gunshot wound. Different drops of blood hit the ground at different angles.

One way to find the origin of the blood from the distribution pattern of the blood streaks. This can be done by using knowledge of trigonometry to consider the path of motion.

It will set the path of movement to be straight. Gravitational acceleration is not taken into account. In practice, blood streak distribution pattern analysis uses a rope to anchor the point of the blood streak to the site of the streak. or use a computer program to analyze This calculation uses only the basic knowledge of trigonometry, with the following steps:

Identify the appropriate bloodstain group and calculate the angle of incidence of this bloodstain.
Consider the intersection of the lines drawn through the longest axis of symmetry of the surface blood streak.
Consider the intersection of the trajectories of converging bloodstains in three-dimensional space. or consider looking for the origin of the blood
In calculating the origin of blood, two blood marks must be considered, as in the following example.

Example 2

Mayhem occurred in the room. When the police arrived at the scene, neither the assailant nor the victim could be found. But a number of blood marks were found on the walls. in order to find the point where the victim was attacked

The forensic staff therefore selected 2 blood marks, namely blood marks A and blood marks B, which from the examination revealed that blood marks A were 3.8 mm wide and 5 mm long, blood marks B were 4.5 mm wide and 5.7 mm long, were blood marks A and blood marks B. 75 cm apart when passing through the longest axis of symmetry of blood marks A and blood marks B, intersect at point C as shown in Figure 5. When measuring the dimensions of angles A and B, α = 65 o and β = 80 o . In order, find the distance from the wall where the victim was attacked.

Note that points A, B, and C are on the same plane. Which may be on the floor or the wall. As mentioned above, it is not difficult to find a position where there is an attack. But finding the location of the attack was not enough to stand trial. This requires other important evidence such as fingerprints, and identification of the perpetrator’s DNA at the scene. Finding the size and type of insects on the corpse, which will know the time of death and may also indicate the crime scene, so those who study forensic science must be well-versed in mathematics. and various fields of science

From this article, we will see that we can apply knowledge of basic mathematics to help solve existing crimes. The author therefore hopes that this article will inspire readers to find ways to apply mathematics to solve other problems in real life. Next time, the author will bring an interesting story to share. listen again