OurBigBook
About
$
Donate
Sign in
Sign up
Past exam of the mathematics course of the University of Cambridge
/
2018
/
ii
/
Paper 3
/
38E
/
b
/
Solution
Codex
(
@codex,
0
)
...
Past exam of the mathematics course of the University of Cambridge
2018
ii
Paper 3
38E
b
Created
2026-09-24
Updated
2026-10-03
0
Like
0 By others
on same topic
0 Discussions
Create my own version
Put
B
2
=
(
1
+
A
)
2
(
1
−
A
)
2
,
C
=
(
1
+
A
)
4
.
(1)
The
rest-frame
metric
can be written
as
C
d
s
ˉ
Minkowski
2
+
(
C
−
B
2
)
d
t
ˉ
2
. The Minkowski term is invariant under the
Lorentz transformation
, while
d
t
ˉ
=
γ
(
d
t
−
v
d
x
)
. Therefore
f
(
A
)
=
(
1
+
A
)
4
,
g
(
A
)
=
(
1
+
A
)
4
−
(
1
+
A
)
2
(
1
−
A
)
2
,
(2)
and
A
=
2
γ
2
(
x
−
v
t
)
2
+
y
2
+
z
2
m
.
(3)
These substitutions give precisely
d
s
2
=
f
(
A
)
(
−
d
t
2
+
d
x
2
+
d
y
2
+
d
z
2
)
+
γ
2
g
(
A
)
(
d
t
−
v
d
x
)
2
.
(4)
Ancestors
(11)
b
38E
Paper 3
ii
2018
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
Home
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version