# 7 Real-life Applications Of Mathematical Induction

Mathematical induction is a widely used mathematical concept that has varied real-life applications. The history of mathematical induction can be traced back to 1909, and the father of mathematical induction is an Italian mathematician called Giovanni Vacca. Inductive and deductive reasoning are crucial for teaching though major mathematical concepts including mathematical induction is based on deductive reasoning and it is also one of a rigorous mathematical concept.

Principles of Mathematical induction are applied to various scientific fields. In this article, we have discussed the real-life application of mathematical induction and some fields where mathematical induction is commonly used.

Before beginning, let’s see what mathematical induction is.

## What is mathematical induction?

Mathematical induction is among the various mathematical propositions used to prove statements or theorems true related to natural numbers (n).

In simple terms, mathematical induction is used to prove that a particular statement is true regarding a natural number and then prove that the statements following the first statement are also true for the following natural numbers.

To prove the statements or theorems true, follow the two steps:

Step 1: Base step- Prove that the first statement is true, n=1; therefore, P(1) is true.

Step 2: Inductive Step- Prove that if the first statement is true, then the next is also true; that is, if n=k, where k is any natural number, the statement also stands true for n=k+1. Hence, the p(k+1) is also true.

Let’s understand mathematical induction through an example.

For instance, you are standing in a queue to order a burger. The person first in line orders a regular burger, and the second one also orders the same. What are the chances that the third person in the queue will order the same? Using mathematical induction, we can conclude that there is a high chance that the third and other person behind him will also order a regular burger.

That’s mathematical induction in real-life!

Let’s simplify the same example in mathematical terms.

The first person in the queue orders a regular burger; n=1 or P(1) is true.

Now let’s say k=50

Assuming that P(K) is 50 and is true, we can deduce that P(K+1) will also be true.

## Real-life applications of mathematical induction

Some real-life applications of mathematical induction are-

### 1. Solving puzzles

The principle of mathematical induction applies to Solving puzzles. To solve a puzzle, we need n number of moves, where n is a natural number. For solving a complete puzzle, we can assume we need n+1 moves. Hence, mathematical induction.

### 2. Domino effect

Another real-life application of mathematical induction is the toppling of dominoes. You will push one domino piece, and all the other pieces will follow. Here, the action of the first piece determines the action of all other pieces. The only condition is all the pieces should be arranged at an equal distance.

### 3. Sinking of Titanic

Another classic application of mathematical induction can be found in a real-life scenario- the sinking of the Titanic. The Titanic had various compartments, and when the Titanic was hit by a glacier, the first compartment was the first to be filled with water. After that, it was common that all the compartments would follow, and the ship would eventually drown.

### 4. Tower of Hanoi

The Tower of Hanoi explains various mathematical phenomena, including mathematical induction. To solve the problem of the Tower of Hanoi, one has to move the first disc, followed by the second, and third, and so on. Here, the action of the first disc determines the action of other discs. Hence, mathematical induction.

### 5. Common knowledge using inductive reasoning

Another great application of mathematical induction is common knowledge. To solve some real-life problems, we act (n=1), and the action of the first step determines the other step.

### 6. Gas stations on highways

On various long highways, gas stations are generally located at equal distances for travelers’ convenience. For instance, a person fills his car with fuel at the first gas station, and his car can now travel for 25 km. The second gas station is 20 km away from the first. Therefore, the person has to refill his fuel at the second gas station. Hence, mathematical induction.

### 7. Zipping a zipper

Another real-life application of mathematical induction is zipping a zipper. Zip the first tooth of a zipper, and the other teeth will follow the same manner, indicating mathematical induction.

## Mathematical induction and its application in different fields

Mathematical induction has its application in various scientific and mathematical fields. Some areas where mathematical induction is commonly used are-

### 1. Electrical engineering

The principles of mathematical induction have their application in the field of electrical engineering. Mathematical induction is used to analyze the successful operations of circuits and the sequence of circuits. Additionally, mathematical induction is utilized to prove the characteristics and properties of circuits.

### 2. Computer science and Algorithms

Solving algorithm-related problems requires mathematical induction. Mathematical induction comes in handy in identifying the efficiency and correctness of algorithms used in various computer science programs.

### 3. Probability

Probability is a branch of mathematics, and solving probability-related questions requires mathematical induction. An equation of mathematical induction is used to identify the probability of occurrence of a certain event or phenomenon.

### 4. Counting arrangements

Mathematical problems requiring sequencing numbers activities or solving the arrangements requires mathematical induction. Mathematical induction is further useful for deriving the formula from the arrangements.

### 5. Number theory

Number theory is another widely used mathematical concept that applies to integers, prime numbers, congruences, etc. Mathematical induction is used to solve theorems and prove the validity of statements true for natural numbers.

## Concluding thoughts

Mathematical induction is a widely used mathematical concept used in various scientific fields. Mathematical induction is one of the basic methods to prove a given theorem or statement and write a proof of it. Since mathematical induction is based on deductive reasoning, we deduce the given statements related to natural numbers as true and prove them as true.