# Felix-is-not-Klein conjecture

**Biradical numbers** are those numbers that are obtained recursively from *1* by addition *x+y* , multiplication *x.y* , negativation* -x* , reciprocation *1/x *for *x* not *0* and biradication *sr(x)* of nonnegative numbers, meaning square root (contrary to the Bavarian notation of the included publications here conventional notation is used for functions).

**Felix-numbers** are the biradical numbers inside the interval from *-1* to *1* (without the limits).

**Klein-numbers** are constructed on the basis of the Euclidean Klein-model of Lobachevsky geometry. Klein-numbers are biradical numbers that are obtained recursively:

starting from *sr(2sr(2)-2) *by successive application of

annition *(x+y)/(1+x.y)*

menition *-x*

evition * x.y/(y+z)* where *(x.x+y.y)<1* and not *y+z=0*

riation *sr(x.x+y.y-x.x.y.y*)

clarition *sr((x.x-y.y)/(1-y.y)*) where not* x.x<y.y *

jacition *(1-sr((1-y.y.(1-x.x))/(1-z.z)))/x* where not *x=0* , else equal *0*

Klein-numbers lie inside the interval from *-1* to *1* (without the limits) by construction.

Klein-numbers are Felix-numbers.

**Conjecture: not all Felix-numbers are Klein-numbers**

It looks quite obvious, however, a proof is needed. It is sufficient to show that* 1/2* is not a Klein-number. If you have a proof, please contact the author !

With two Felix-numbers as coordinates one gets the points of the Felix-circle

With two Klein-numbers as coordinates one gets the points of the Klein-circle.