MathDB

A calculating ruler is a ruler for doing algebric calculations. This ruler has three arms, two of them are sationary and one can move freely right and left. Each of arms is gradient. Gradation of each arm depends on the algebric operation ruler does. For eaxample the ruler below is designed for multiplying two numbers. Gradations are logarithmic. http://aycu05.webshots.com/image/5604/2000468517162383885_rs.jpg For working with ruler, (e.g for calculating

x.y

) we must move the middle arm that the arrow at the beginning of its gradation locate above the

x

in the lower arm. We find

y

in the middle arm, and we will read the number on the upper arm. The number written on the ruler is the answer. 1) Design a ruler for calculating

x^{y}

. Grade first arm (

x

) and (

y

) from 1 to 10. 2) Find all rulers that do the multiplication in the interval

[1,10]

. 3) Prove that there is not a ruler for calculating

x^{2}+xy+y^{2}

, that its first and second arm are grade from 0 to 10.

Problem Statement