Induction in Geometry

Given: a unit length.

Use only a straightedge (ruler without markings) & a compass.
Prove: we can construct a line segment of √n for all n ∈N.
Proof:
1) n=1 (given).

2) Assume true for n, i.e. can construct √n

3) Construct a right-angled triangle with height = 1, base= √n

=>  hypotenuse  = \sqrt {n+1}
=> True for n+1

Therefore true for all n ∈N [QED]

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s