With Meter Scale of mm- precision and Compass, how do you mark exactly #x = sqrt k# cm, k = 2, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 10, 21, 22, 23, 24, 26, ... and 99?

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Answer 1 · 2018-08-09T03:25:40

See illustrative graph and proof.

Excerpt from my document:

Mark B (0, k - 1/4 ) on the y-axis.

With B as center, make a circular arc of radius k + 1/4, to cut the x-

axis #larr#, at K.

OK. OK = sqrt k, k = 1, 2, 3, 4, 5, ...#

Of course, the meter scale can mark upto k = 99 and th compass

arm should be #50sqrt2# cm long.

Proof:

#sqrt ( ( k + 1/4 )^2 - ( k - 1/4 )^2) = sqrt k#.

Example: k = 11. OB = 9.75 and BK = 11.25. OK = sqrt11#.

graph{((x-sqrt11)^2 + y^2- 0.02) (x^2 + (y-9.75)^2-0.032)(x^2+ (y-9.75)^2- (10.25)^2)=0[-2 22 -1 11] }.

The accuracy is directly proportional to pixel dimensions, in any

graphic resolution.

Of course, marking a point, that is in #epsilon = 0_+# space, is

impossible.