The third idea in Pascal’s triangle is that it contains hidden sequences. For instance, the first two columns are not that much significant; they are merely the natural numbers and ones. The third column is comprised of triangular numbers. That is, you can consider the number of triangular numbers as the number of dots that are used to make different sized triangles. Similar to this case, the fourth column comprises of tetrahedron number. In other words, the column represents a triangular pyramidal number. As suggested by their name, they present the numbers of dots that will be required to complete a pyramid with a base that is triangular. The sequences follow in an order describing the “simplices” which are extrapolations of the triangle or tetrahedron idea extending to arbitrary dimensions.

Applications of Pascal Triangle in Real World

There are countless applications of the Pascal triangle in the real world. The first application is that Pascal triangle is applied to establish the IP addresses. In computing, the application of binomial theorem is inevitable today. Binomial theorem is a fundamental method that is used to distribute IP Addresses. It makes it possible to distribute not only the IP Addresses but also the virtual IP Addresses. In this case, binomial theorem is used to distribute bits to ensure that all hosts are covered in the IP address. This situation occurs when the number of the host is more than the total round off of the given IP address of the fixed host.

Pascal triangle is also applied in architecture. In this case, by the use of probability computation, the architects can quickly determine the amount of the raw materials and labor that is required to finish the project. The probability calculation can also be used to determine the shape of the building structure and the type of inputs that will be appropriate. For example, one can determine the frequencies and intensity of certain natural phenomena such as flooding, landslides, and other valuable information that is likely to affect infrastructures and buildings.  With this information at hand, chances of losses of both property and lives of people will be highly reduced. In addition to this, the calculation can also help the investors in those structures to determine the cost of the complete project hence reduce chances of failing to see through the project. It helps the engineers to develop accurate estimates regarding the time and cost required for project completion by calculating the magnitude of a project (Kolosov, 2018). It also helps the contractors to deliver competent projects that will be profitable.

Pascal triangle is a vital tool in the insurance companies. In this case, the insurance company must determine the possibility of particular risk to occur. The strategy that is mainly applied here is by assessing the probability of a given chance to happen leading loss. Generally, the areas in which the risk is highly anticipated to occur will drive the insurance company to ask for high premiums from the company’s clients. Taking an example, a public vehicle is likely viewed to be at high risk of getting involved in an accident than the private cars. The reason behind this is just because risks are directly proportioned to the time spent on the roads. Therefore, the probability will enable the insurance company to make sound decision hence reduce chances of incurring losses.

Conclusion

In conclusion, the Pascal triangle and its application play a vital role in the modern world. Its use covers every aspect of life; socially economically. The method such as binomial theorem has enabled people and businesses to determine the possibility of a particular situation to occur. Having this knowledge in mind, people have an unobstructed view of the case and make a favorable decision. The awareness enables people to come up with strategies that will assist them to avoid much harm in the future. The Pascal triangle and its application, has given people a positive attitude towards life by improving trust in different areas. Improved confidence is mainly as a result of predicting how the future is likely to be using the already experienced situation.

References

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