Question: Show that n circles divide the plane into n2 n + 2 regions if every two circles intersect in exactly two points and no

Show that n circles divide the plane into n2 − n + 2 regions if every two circles intersect in exactly two points and no three circles contain a common point.

Step by Step Solution

★★★★★

3.40 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We will prove by induction that n circles divide the plane into n 2 n 2 regions One circle certainly ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

923-M-C-M-S (1901).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Use mathematical induction to show that when n circles divide the plane into regions, these regions can be colored with two different colors such that no regions with a common boundary are colored...

Recall that the axes divide the plane into four quadrants as shown. For following Exercises if a and b are both positive numbers, determine whether each statement is true or false. 1. (-a, -b) lies...

In this exercise, we shall prove that the three assumptions underlying the Poisson process model do indeed imply that occurrences happen according to a Poisson process. What we need to show is that,...

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

I need help with this lab. Please answer questions for pages 4-7. Freefall Purpose: We will measure the value of 'little g', or the acceleration due to gravity on the surface of Earth. The particular...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Intervals Intervals are extents of time or one-dimensional space. They form the basis of many applications such as appointment calendars, geographic information systems, and graphics programs. For...

2. For which of the following reactions. Equilibrium constant (k) is less than unity? (a) (CD3)C-H+ (CH3)3C (CD3)3C +(CH3)3C-H 0 (b) + NH = + CH4 (c) CH3-CEC-H+NH CH3-CEC : + NH3 e (d) + NH > + NH3

Assuming that air resistance is unimportant, calculate the minimum velocity a particle must have at the surface of Earth to escape from Earths gravitational field. Obtain a numerical value for the...

Consider the following independent activities: a. Payment of a cash dividend b. Amortization of intangible asset c. Gain on disposal of equipment d. Exchange of common stock for land e. Increase in...

6. A test consists of five true-false questions. (a) In how many ways can it be completed? (Hint. The task of answering five true-false questions consists of five stages.) (b) A correctly answered...

Exercise 6-13 presented the joint temperatures of the O-rings (F) for each test firing or actual launch of the space shuttle rocket motor. In that exercise you were asked to find the sample mean and...

An article in the Transactions of the Institution of Chemical Engineers (Vol. 34, 1956, pp. 280293) reported data from an experiment investigating the effect of several 31 F2 process variables on the...

The cold start ignition time of an automobile engine is being investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.75, 1.92, 2.62, 2.35, 3.09,...

Ashley Limiteds overhead costs of $700,000 consist of machining $400,000; inspecting $200,000; and packaging $100,000. Machining works 4,000 hours a year, 500 inspections occur each year, and 1,000...

ANSWER ALL FOR THUMBS IF ONLY ONE IS ANSWERED I WILL GIVE THUMBS DOWN 1.1 1.2 1.3 (Yield to maturity) Fitzgerald's 15-year bonds pay 11 percent interest annually on a $1,000 par value. If the bonds...

what is the answer? please and thanks. A stock is trading for a share price of $21.61. You expect it to pay a dividend of $136 exactly one year from now, and you expect future annual dividends to...