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下面列举的问题，没有排版好。以后有时间再慢慢完善
1，
Four Hinged Squares
The purpose of the applet below is to illustrate an 1826
sangaku
hung by Ikeda Sadakazu in an Azabu shrine, Tokyo. The tablet since
disappeared but not before it was recorded in an 1827 book
Shamei Sanpu (Sacred Mathematics) by Shiraishi
Nagatada (1795-1862). The problem has also been included in an 1840
collection Sanpo Chokujutsu Seikai (Mathematics
without Proof) by Heinouchi Masaomi.
Four squares are hinged as shown. When points A, B, C are
collinear, what is the relationship between the sides of squares
BEKH and KINS?
2，Given four mutually tangent circles with curvatures a,
b, c, and d, the Descartes circle equation
specifies that 2(a2
b2
c2 d2)
= (a b c
d)2.
3，Given three tangent circles, there are precisely two additional
circles that are tangent to all three. If the original circles have
curvatures a, b, and c, and the additional
circles have curvatures d and d', the following
simple relationship holds: d d' = 2(a
b c).
4，
Chords KN and ST are perpendicular to diameter CP of a circle
with center O at points Q and R. SQ intersects the circle in V. (K,
S are on one side of CP, N and T on the other. Q is between P and
R.) Let q be the radius of the circle inscribed into the
curvilinear triangle TQV. Prove that
(1)
1/q = 1/PQ 1/QR
.
5，
The applet purports to suggest
the following sangaku [Temple
Geometry, p. 3]:
Assume points A and B are fixed on a line AB and two circles
are drawn touching AB at A and B and tangent to each other. A
circle Q is tangent to AB and the two circles externally. Prove
that, as the two circles change, circle Q remains tangent to a
fixed circle through A and B. Moreover, the radius of the latter is
5/8·AB.
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