(共14张PPT)
What’s
Euler’s
puzzle?
Koningsberg
is
an
island
and
there
is
a
river
breaking
it
into
two
parts.
“Seven
Bridges
of
Konigsberg”
and
the
famous
“Euler
path”.
People
wondered
if
they
could
walk
around
the
city
by
crossing
the
seven
bridges
without
going
over
any
of
them
twice
or
going
back
on
himself,
but
Euler
found
he
couldn’t
cross
all
the
seven
ones.
This
is
Euler’s
puzzle.
The
first
stage
in
his
research
is
to
find
the
problem
that
he
could
cross
six
of
the
bridges
without
going
over
any
of
them
twice
or
going
back
on
himself,
but
he
couldn’t
cross
all
seven.
How
did
Euler
prepare
for
his
research?
The
second
stage
is
to
think
of
a
method:
He
drew
a
map
and
used
dots
and
lines
to
simplify
his
analysis.
Trying
and
observing
over
and
over
again,
he
found
a
general
rule.
It
is
topology.
Euler’s
theory
is
called
“The
Euler
path”,
which
is
expressed
like
this:
If
a
figure
has
more
than
two
odd
points,
you
cannot
go
over
it
without
lifting
your
pencil
from
the
page
or
going
over
a
line
twice.
What
are
the
theories?
So
the
general
rule
that
Euler
found
is
the
even
points
and
the
odd
points.
Look
at
the
following
pictures:
Conclusion
Euler’s
theory
(一笔画)
可以一笔画只有两种情况：
1.
没有奇数顶点。
2.
只有两个奇数顶点。(共19张PPT)
Robert
Briggs
is
very
interested
in
biology
and
especially
in
the
study
of
plants.
Today
he
is
telling
his
friend
Zhang
Wei
some
exciting
news.
Before
you
listen
to
the
tape
discuss
with
your
partner
how
you
would
find
out
the
name
of
a
flower.
New
words
in
the
listening
passage:
species
种类
parrot
鹦鹉
blackbird
乌鸦
Now
listen
to
the
tape.
1.
Which
of
the
following
statements
describes
what
this
listening
passage
is
about?
Give
your
reasons.
A.
This
is
about
a
man
who
wants
to
name
a
flower.
B.
This
is
about
a
man
who
finds
a
flower
and
wants
to
own
it.
C.
This
is
about
a
man
who
finds
a
flower
and
wants
to
know
if
it
is
a
new
species
of
flower.
It
does
not
give
enough
information.
B
is
inaccurate.
Listen
to
the
tape
again
and
complete
the
following
passage.
To
find
the
name
of
an
unknown
flower
first
you
should
ask
your
_______
teacher
to
help
you.
He
/She
will
look
in
a
special
_____
written
by
Carl
Linnaeus.
He
lived
in
_______
from
____
to
_____.
biology
book
Sweden
1707
1778
He
was
very
important
because
he
solved
a
_______
problem
for
biology.
serious
Listen
to
the
tape
for
the
third
time
and
answer
these
questions.
1.
If
Robert
Briggs
finds
the
flower
in
the
book,
what
does
that
mean?
It
means
that
his
flower
has
already
been
identified
and
has
a
name.
2.
How
would
he
know
if
his
lily
is
a
new
species?
He
would
know
by
checking
his
lily
against
other
lilies
in
the
specialist
book.
If
his
lily
is
different
it
will
be
a
new
species.
3.
Why
do
plants
all
have
two
names?
All
plants
have
two
names
just
like
people.
The
first
is
the
group
of
flowers
they
belong
to
and
is
like
the
family
name.
The
second
is
the
kind
of
flower
within
that
group
and
is
like
a
given/personal
name.
4.
What
was
the
serious
problem
for
biology
that
Linnaeus
solved?
Before
Linnaeus
there
was
no
way
of
finding
out
whether
a
plant
was
new
or
not.
This
caused
problems
because
different
scientists
claimed
that
they
had
found
and
named
flowers
first.
After
he
organized
his
system
it
was
easy
to
discover
whether
a
plant
was
new
or
not
and
so
who
had
the
right
to
name
it.
Make
a
list
of
all
the
great
mathematicians
that
you
know
of
or
have
learned
about.
What
do
you
know
of
their
achievements?
Leonhard
Euler
(1707-1783)
Nationality
Swiss
Fields
Mathematician
and
Physicist
pure
(纯的)
symbol
(符号)
Л
(圆周率)
sine
(正弦)
cosine
(余弦)
topology
(拓扑学)
angle
(角)
diagram
(图表)
Read
the
words
below
and
learn
to
pronounce
them
correctly.
pure
(纯的)
symbol
(符号)
Л
(圆周率)
sine
(正弦)
cosine
(余弦)
topology
(拓扑学)
angle
(角)
diagram
(图表)
Listen
to
Part
1
and
tick
the
words
below
that
Euler
introduced
into
mathematics.
Listen
to
Part
2
and
fill
in
the
chart
below.
topology
introduced
many
new
symbols
into
maths
wrote
more
books
than
anyone
before
or
since
discovered
a
new
branch
of
mathematics
Euler’s
new
branch
of
mathematics
Why
Euleer
is
considered
to
be
a
great
mathema-
tician
What
was
the
problem
of
the
city
of
Konigsberg?
It
had
a
river
running
through
it.
The
centre
of
Konigsberg
is
an
island
and
as
it
passes
the
island
the
river
breaks
into
two
parts.
Seven
bridges
were
built
so
that
the
people
of
the
city
could
get
from
one
part
to
another.
The
people
wondered
if
you
could
walk
around
the
city
so
that
you
would
cross
each
bridge
only
once.
