Linear Algebra: Norm puzzles in the two-dimensional plane

Some puzzles concerning norms in the plane. You can play freely with the figures.

Puzzle 1

What is the norm used in the following dynamic sketch?

This page requires a Java capable browser. The norm is:
a) The ordinary euclidean 2-norm.
b) The taxi cab norm, the 1-norm.
c) The infinity-norm.
d) A p-norm with p > 2.
e) It is not a norm. Why?

Puzzle 2

What is the norm used in the following dynamic sketch?

This page requires a Java capable browser. The norm is:
a) The ordinary euclidean 2-norm.
b) The taxi cab norm, the 1-norm.
c) The infinity-norm.
d) A p-norm with p > 2.
e) It is not a norm. Why?

Puzzle 3

What is the norm used in the following dynamic sketch?

This page requires a Java capable browser. The norm is:
a) The ordinary euclidean 2-norm.
b) The taxi cab norm, the 1-norm.
c) The infinity-norm.
d) A p-norm with p > 2.
e) It is not a norm. Why?

Puzzle 4

What is the norm used in the following dynamic sketch?

This page requires a Java capable browser. The norm is:
a) The ordinary euclidean 2-norm.
b) The taxi cab norm, the 1-norm.
c) The infinity-norm.
d) A p-norm with p > 2.
e) It is not a norm. Why?

Finally: How well you can draw a p-circle

This page requires a Java capable browser.

For what values of p shall we really have a norm?

Martti.Pesonen@Joensuu.Fi