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School
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3
2
1
Outside the high school program
/ Space geometry: non-cavaliere perspective
8 exercises (100% corrected)
a
A
B
D
E
F
G
H
M
N
P
Ligne d’horizon
a
b
d
h
m
n
1.
Unclassifie
d
financial
ye
ars
E.6746
T
o
mak
e
a
solid
S
,
w
e
cut
out,
from
a
cub
e
of
edge
4
cm
,
a
tetrahedron
(se
e
c
avalier
p
ersp
e
c-
tive
diagr
am
b
elow)
where
M
,
N
and
P
are
the
middles
of
three
edges.
Note
S
the
solid
AB
F
E
D
M
N
P
GH
th
us
obtained.
On
the
app
endix,
w
e
sk
etc
hed
the
v
anishing-p
oin
t
p
ersp
ectiv
e
dra
wing
of
solid
S
,
plane
(
AB
N
M
D
)
b
eing
fron
tal.
P
oin
ts
A
,
B
,
F
,
E
,
D
,
M
,
N
,
P
,
G
,
H
are
represen
ted
b
y
the
lo
w
ercase
named
p
oin
ts
a
,
b
,
f
,
e
,
d
,
m
,
n
,
p
,
g
,
h
.
Complete
the
dra
wing
of
the
solid
represen
tation
S
after
plac-
ing
the
main
v
anishing
p
oin
t
w
.
The
construction
lines
are
left
visible.
E.6743
1
Complete
on
figure
1
,
the
ca
v
alier
p
ersp
ectiv
e
repre-
sen
tation
of
ratio
1
2
of
v
anishing
angle
30
o
of
a
cub
e
AB
C
D
E
F
GH
whose
fron
tal
plane
AB
F
E
has
b
een
giv
en.
2
Complete
on
figure
2
,
the
v
anishing-p
oin
t
p
ersp
ectiv
e
represen
tation
of
a
cub
e
AB
C
D
E
F
GH
whose
fron
tal
plane
AB
F
E
,
p
oin
t
C
and
v
anishing
p
oin
t
O
ha
v
e
b
een
giv
en.
3
Name
one
prop
ert
y
of
the
ca
v
alier
p
ersp
ectiv
e
represen-
tation
that
is
not
v
erified
in
v
anishing-p
oin
t
p
ersp
ectiv
e.
4
Complete
on
figure
3
,
the
v
anishing-p
oin
t
p
ersp
ectiv
e
represen
tation
of
a
regular
tiling
of
four
ro
ws
of
six
tiles.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6746
sacados/6746
A
B
D
E
F
G
H
M
N
P
Ligne d’horizon
a
b
d
h
m
n
chapExoCorrec/6743
sacados/6743
Japon Juin 2003 5 points
A
B
F
E
Figure 1
A
B
F
E
O
C
Figure 2
Figure 3
A
B
C
D
A
B
C
D
E.6745
A
square
plate
AB
C
D
has
b
een
dra
wn
in
p
ersp
ectiv
e
at
t
w
o
leak
age
p
oin
ts
on
the
dra
wing
b
elo
w
:
1
Sho
w
the
horizon
line
of
this
p
ersp
ec-
tiv
e
on
the
dra
wing
ab
o
v
e.
2
Dra
w
on
this
plate
a
c
hec
k
erb
oard
of
sixteen
square
squares
as
sho
wn
in
the
figure
b
elo
w
(you
c
an
use
the
p
oint
of
interse
ction
of
the
diagonals
of
the
squar
e
AB
C
D
and
the
two
vanishing
p
oints)
.
h
ttps:/
/c
hingmath.fr
A
B
F
E
Figure 1
A
B
F
E
O
C
Figure 2
Figure 3
chapExoCorrec/6745
sacados/6745
A
B
C
D
A
B
C
D
A
B
C
D
E
F
G
H
M
N
L
E.6747
An
arc
hitect
b
egan
dra
wing
a
cor-
ridor
(se
e
figur
e
b
elow)
.
He
drew
a
large
rectangular
windo
w
on
the
righ
t
v
ertical
w
all.
He
has
dra
wn
only
part
of
the
flo
or
tiling.
It
is
assumed
that
the
arc
hitect
is
follo
wing
the
rules
of
v
anishing-p
oin
t
p
ersp
ectiv
e.
All
constructions
are
to
b
e
made
on
the
figure
giv
en
in
the
app
endix
to
b
e
returned
with
the
cop
y
.
1
Name
one
rule
of
v
anishing-p
oin
t
p
ersp
ectiv
e.
Chec
k
it
on
the
figure
pro
vided
b
elo
w.
(we
c
an
p
ossibly
p
erform
c
onstructions
on
the
figur
e)
.
2
Kno
wing
that
the
tiling
is
regular,
represen
t
the
3
first
ro
ws
of
5
tiles
(le
ave
c
onstruction
lines
cle
arly
visible
;
no
written
justific
ation
is
otherwise
r
e
quir
e
d)
.
3
The
rectangular
windo
w
on
the
righ
t-hand
w
all
has
t
w
o
sashes
of
equal
width
separated
b
y
a
v
ertical
rail.
A
han-
dle
is
fixed
in
the
middle
of
this
v
ertical
crosspiece.
Only
the
windo
w
frame
is
sho
wn
in
the
dra
wing.
Complete
the
figure
b
y
represen
ting
the
v
ertical
crosspiece
b
y
a
segmen
t
and
the
handle
b
y
a
p
oin
t
M
.
E.6748
The
dra
wing
b
elo
w
sho
ws
a
house
in
parallel
p
ersp
ectiv
e.
AB
C
D
E
F
GH
is
a
righ
t-angled
prism
whose
faces
AB
C
D
and
E
F
GH
are
horizon
tal
and
form
the
flo
or
and
ceiling
of
the
house,
resp
ectiv
ely
.
The
edge
[
AE
]
is
therefore
v
ertical.
The
t
w
o
faces
AB
C
D
and
E
F
GH
are
squares.
E
F
GH
N
L
is
a
righ
t
prism
;
the
base
E
F
N
of
this
righ
t
prism
is
an
isosceles
triangle
at
N
whose
heigh
t
[
N
M
]
is
suc
h
that
N
M
=
AE
.
In
this
exercise,
w
e
agree
to
lab
el
a
p
oin
t
in
space
with
a
cap-
ital
letter
and
to
lab
el
its
image
in
a
cen
tral
p
ersp
ectiv
e
with
a
lo
w
ercase
letter
(so
a
is
the
image
of
A
,
b
is
the
image
of
B
)
.
No
justific
ation
of
the
c
onstructions
is
exp
e
cte
d,
but
the
c
onstruction
lines
wil
l
b
e
left
visible.
1
A
cen
tral
p
ersp
ectiv
e
represen
tation
of
this
house
is
started
in
figure
1
b
elo
w.
The
horizon
line
and
the
main
v
anishing
p
oin
t
w
are
dra
wn.
The
w
all
AB
F
E
is
assumed
to
b
e
in
a
fron
tal
plane.
a
Using
the
represen
tation
of
the
diagonals
of
squares
AB
C
D
and
E
F
GH
,
construct
the
distance
p
oin
ts
d
1
and
d
2
of
this
cen
tral
p
ersp
ectiv
e
represen
tation
on
the
dra
wing
in
figure
1
b
Complete
the
represen
tation
of
the
house
in
this
cen-
tral
p
ersp
ectiv
e
on
this
figure.
c
Place
the
image
i
of
the
middle
I
of
[
AE
]
as
w
ell
as
the
image
j
of
the
middle
J
of
[
C
G
]
.
Through
whic
h
p
oin
t
should
the
line
(
ij
)
pass?
2
Another
cen
tral
p
ersp
ectiv
e
represen
tation
of
the
house
is
started
in
figure
2
.
P
oin
ts
w
and
w
are
the
resp
ectiv
e
v
anishing
p
oin
ts
of
lines
(
AB
)
and
B
C
)
.
Complete
the
dra
wing
2
of
the
house
in
this
new
cen
tral
p
ersp
ectiv
e.
3
Name
t
w
o
prop
erties
of
parallel
p
ersp
ectiv
e
that
are
not
v
erified
b
y
cen
tral
p
ersp
ectiv
e.
Illustrate
them
b
y
refer-
ring
to
the
represen
tation
giv
en
at
the
b
eginning
of
the
exercise
and
those
completed
in
figures
1
and
2
.
Figure
1
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6747
sacados/6747
chapExoCorrec/6748
sacados/6748
A
B
C
D
E
F
G
H
M
N
L
a
b
c
e
f
g
n
m
w
w
w
a
b
c
e
f
g
A
B
D
Figure
2
E.6744
The
figure
b
elo
w
sho
ws
the
v
anishing-p
oin
t
p
ersp
ectiv
e
plot
of
the
AB
D
isosceles
righ
t-
angled
A
triangle
and
the
horizon
line
Δ
of
the
plane
of
this
triangle.
All
constructions
requested
m
ust
b
e
carried
out
on
this
sheet
and
justified
on
the
cop
y
.
1
Place
the
v
anishing
p
oin
t
F
1
,
of
the
direction
of
the
line
(
AB
)
,
the
v
anishing
p
oin
t
F
2
of
the
direction
of
(
B
D
)
and
F
3
,
that
of
the
direction
of
(
AD
)
.
2
Construct
the
p
oin
t
C
suc
h
that
AB
C
D
is
a
square.
3
Construct
the
p
oin
t
E
,
iamge
of
the
p
oin
t
C
b
y
symme-
try
of
cen
ter
D
.
4
Construct
p
oin
t
J
,
midp
oin
t
of
segmen
t
[
AD
]
.
h
ttps:/
/c
hingmath.fr
a
b
c
e
f
g
n
m
w
w
w
a
b
c
e
f
g
chapExoCorrec/6744
sacados/6744
A
B
D
a
b
c
d
e
f
g
h
E.6749
On
eac
h
of
the
faces
of
a
AB
C
D
E
F
GH
cub
e,
there’s
a
square
pattern
formed
b
y
the
middles
of
the
sides
of
the
faces
:
Belo
w
is
a
cen
tral
p
ersp
ectiv
e
represen
tation
of
the
cub
e
AB
C
D
E
F
GH
,
whose
face
AB
F
E
lies
in
a
fron
tal
plane.
The
square
inscrib
ed
in
the
AB
F
E
face
is
represen
ted
there.
The
images
of
the
p
oin
ts
A
,
B
,
C
.
.
.
are
noted
in
lo
w
er
case
letters
a
,
b
,
c
.
.
.
The
line
(
p
)
is
the
horizon
line.
The
constructions
requested
will
b
e
carried
out
on
the
figure
b
elo
w.
Useful
construction
lines
should
b
e
left
visible.
1
a
Construct
the
main
v
anishing
p
oin
t
r
.
b
Construct
the
t
w
o
distance
p
oin
ts
s
and
t
.
2
a
Construct
the
image
i
of
the
midp
oin
t
I
of
the
seg-
men
t
[
C
G
]
.
b
Construct
the
image
j
of
the
middle
J
of
the
segmen
t
[
B
C
]
.
c
Prop
ose
a
v
erification
of
the
construction
of
the
p
oin
t
j
d
Complete
the
dra
wing
of
the
squares
sho
wn
on
the
t
w
o
visible
faces
of
the
cub
e.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6749
sacados/6749
Extrait d'Antilles-Guyanne Septembre 2007
a
b
c
d
e
f
g
h
D
H
C
G
A
B
E
F
S
A
B
C
D
E
F
G
H
E.6750
Throughout
this
exercise,
capital
letters
will
b
e
used
to
designate
p
oin
ts
in
space
and
lo
w
ercase
letters
to
designate
flat
represen
tations
of
those
p
oin
ts.
F
or
example,
a
represen
ts
A
.
All
constructions
will
b
e
made
on
the
figure
giv
en
b
elo
w.
No
justification
for
the
constructions
is
exp
ected,
but
the
con-
struction
lines
will
b
e
left
visible.
The
final
represen
tation
will
b
e
traced
in
b
old
or
color
to
im-
pro
v
e
readabilit
y
.
The
figure
giv
en
at
the
end
of
the
exercise
sho
ws
the
cen-
tral
p
ersp
ectiv
e
dra
wing
of
a
cub
e
AB
C
D
E
F
GH
placed
on
a
horizon
tal
plane
with
its
face
AB
C
D
in
a
fron
tal
plane.
1
The
main
v
anishing
p
oin
t
of
this
cen
tral
p
ersp
ectiv
e
rep-
resen
tation
is
called
w
.
Construct
p
oin
t
w
.
2
P
oin
ts
d
1
and
d
2
are
called
the
distance
p
oin
ts
of
this
cen
tral
p
ersp
ectiv
e
represen
tation.
Construct
d
1
and
d
2
,
then
dra
w
the
horizon
line.
3
The
figure
b
elo
w
sho
ws
a
ca
v
alier
p
ersp
ectiv
e
represen
ta-
tion
of
the
assem
bly
describ
ed
in
this
question.
a
Behind
cub
e
AB
C
D
E
F
GH
,
against
face
E
F
GH
,
place
a
second
cub
e,
iden
tical
to
the
first.
Dra
w
this
second
cub
e
on
the
figure
b
elo
w
b
On
the
upp
er
face
of
the
cub
e
AB
C
D
E
F
GH
,
place
a
p
yramid
whose
base
is
the
square
D
C
GH
and
whose
ap
ex
is
p
erp
endicular
to
the
cen
ter
of
this
base.
The
heigh
t
of
this
p
yramid
is
equal
to
the
length
of
one
edge
of
the
cub
e
AB
C
D
E
F
GH
.
Dra
w
this
p
yramid
in
the
cen
tral
p
ersp
ectiv
e
represen-
tation
in
the
figure
b
elo
w.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6750
sacados/6750
D
H
C
G
A
B
E
F
S
A
B
C
D
E
F
G
H
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