in this paper, we construct two new primitive Evans triangles by using the Pell equation x^2-Dy^2=1, and give the two forms of the Evans triangle and the corresponding Evans ratio, we also get a new conclusion that the ratio is an integer from a few different forms of the bottom and high.
In this paper we study the generalization of the Brocard congurations.
The denition of q-period broken line is given and then the new necessary and
sucient condition about the existence of two conjugate Brocard points of the
qperiod loop broken line is investigated. Based on the past research, a geometric
method for the construction of all possible loop broken lines with conjugate Brocard
points is developed.
Motivated by Gutkin curves arising in capillary floating and billiard ball problem, we
introduce a new projection function for convex plane curves, and study the curves
when the defined projection function is constant. These curves can be regarded as a
generalization of curves with constant width. We give a necessary and sufficient
condition for the existence of such curves, and provide an explicit expression for the
radius of curvature. Properties of our curves and their relation to Gutkin curves are
also discussed. Finally, we construct and exhibit some curves with constant projection