# Real Life Uses of the Pythagorean Theorem

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Pythagoras is very well known, considering he published no writing during his lifetime. What we know of Pythagoras has come from other philosophers and historians.

Pythagoras was a Greek philosopher and mathematician who is best known for introducing the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is the equivalent of the sums of the squares of the other two legs of the triangle. The theorem is not just a geometric postulate; it also has real world applications.

## Architecture and Construction

The most obvious application of the Pythagorean Theorem is in the world of architecture and building construction, particularly in reference to triangular-shaped roofs and gables. The theorem applies only when dealing with right triangles or triangles with a 90-degree angle.

## Navigation

Triangulation is a method used for pinpointing a location when two reference points are known. When triangulation is used with a 90-degree angle, the Pythagorean Theorem is used to determine the location. Cell phones can be traced by way of triangulation. Car navigation systems use this method. Triangulation can also be used in conjunction with a compass to determine one's geographic location. NASA also uses triangulation to determine the position of spacecraft. NASA sends a signal to the craft which then bounces the signal back. Triangulation uses these figures to calculate the craft's position in space.

## Earthquake Location

Geologists also use the Pythagorean Theorem when tracking earthquake activity. Earthquakes result in two different types of waves -- one that is slower than the other. By triangulating the distance travelled by the faster waves with that travelled by the slower waves, geologists can determine the centre or source of the earthquake.

## Crime Scene Investigation

Forensic investigators use the Pythagorean Theorem to determine bullet trajectory. Bullet trajectory shows the path the bullet took before impact. This trajectory tells police the area from which the bullet originated. Investigators can also tell how close the shooter was to the victim. This can help police determine whether or not a death is a suicide or a homicide. Blood spatter evidence can also be analysed with the Pythagorean Theorem. Blood spatter is the spray of blood from a victim after an assault. Police use these calculations to determine the angle of impact and the positions of both the victim and the assailant during the assault.

## Arrow or Missile Trajectory

Archers use the Pythagorean Theorem to determine the correct trajectory needed to hit a target. If the calculations are accurate, the arrow will hit. If not, the arrow may fall short or miss the mark. Guided missile systems use a similar method to accurately strike their targets.

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- Atlas Quest: Triangulation
- Northwestern University Qualitative Reasoning Group: Navigation
- The Forensic Examiner: Bullet Trajectories -- Misidentifying Converging Bullet Trajectories in Reconstruction
- Gander Mountain: Understanding Arrow Trajectory

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