# Proof by Mathematical Induction : Planes, Lines and Regions

Not what you're looking for?

Suppose that n straight lines in the plane are positioned so that no two are parallel an no three pass throught the same point. Show that they divide the plane into 1/2(n^2 + n + 2) distinct regions.

##### Purchase this Solution

##### Solution Summary

A proof linking lines, planes and regions is provided.

##### Solution Preview

First we prove that how many distinct regions will be created if the n+1th line show up in the plane where there are n lines exist already.

That's will be easy to find that there will be n+1 distint regions created if the n+1th line show ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.