<s>
In	O
plane	O
geometry	O
the	O
Estermann	B-Algorithm
measure	I-Algorithm
is	O
a	O
number	O
defined	O
for	O
any	O
bounded	O
convex	O
set	O
describing	O
how	O
close	O
to	O
being	O
centrally	B-Algorithm
symmetric	I-Algorithm
it	O
is	O
.	O
</s>
<s>
It	O
is	O
the	O
ratio	O
of	O
areas	O
between	O
the	O
given	O
set	O
and	O
its	O
smallest	O
centrally	B-Algorithm
symmetric	I-Algorithm
convex	O
superset	O
.	O
</s>
<s>
It	O
is	O
one	O
for	O
a	O
set	O
that	O
is	O
centrally	B-Algorithm
symmetric	I-Algorithm
,	O
and	O
less	O
than	O
one	O
for	O
sets	O
whose	O
closure	O
is	O
not	O
centrally	B-Algorithm
symmetric	I-Algorithm
.	O
</s>
<s>
It	O
is	O
invariant	O
under	O
affine	B-Algorithm
transformations	I-Algorithm
of	O
the	O
plane	O
.	O
</s>
<s>
The	O
shapes	O
of	O
minimum	O
Estermann	B-Algorithm
measure	I-Algorithm
are	O
the	O
triangles	O
,	O
for	O
which	O
this	O
measure	O
is	O
1/2	O
.	O
</s>
<s>
The	O
curve	O
of	O
constant	O
width	O
with	O
the	O
smallest	O
possible	O
Estermann	B-Algorithm
measure	I-Algorithm
is	O
the	O
Reuleaux	O
triangle	O
.	O
</s>
<s>
The	O
Estermann	B-Algorithm
measure	I-Algorithm
is	O
named	O
after	O
Theodor	O
Estermann	O
,	O
who	O
first	O
proved	O
in	O
1928	O
that	O
this	O
measure	O
is	O
always	O
at	O
least	O
1/2	O
,	O
and	O
that	O
a	O
convex	O
set	O
with	O
Estermann	B-Algorithm
measure	I-Algorithm
1/2	O
must	O
be	O
a	O
triangle	O
.	O
</s>
