id: 06141885
dt: j
an: 2013e.00520
au: Tabachnikov, Serge
ti: The (un)equal tangents problem.
so: Am. Math. Mon. 119, No. 5, 398-405 (2012).
py: 2012
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: G95
ut: convex closed plane curve; oval; tangent
ci:
li: doi:10.4169/amer.math.monthly.119.05.398
ab: Given a circumference and a point lying outside of it, it is well-known
that the two tangents to the circumference passing through the given
point are equal. In this (very interesting) paper the “opposite”
problem (in some sense) is studied. Namely, the author considers a
strictly convex closed plane curve (a.k.a. an oval) and tries to find
(and asks whether it exists) a set of points (maybe a curve) lying
outside it, such that the two tangents to the original oval passing
through each of these points are unequal. The author, against previous
evidence, is able to construct an oval having the desired property.
rv: Antonio M. Oller (Zaragoza)