Mathematics and sports
Ines Kolar
Koprivnica, Croatia
teacher: Mara Grašić
Maths and sports
• we use Maths in sports without even
realizing it
• probabilities, counting, combination and
assessing are the most used calculations
in sports
Maths in football
• Have you ever thought
about using Maths when you
were playing football?
• football requires all
applications of Maths
Team and terrain
Terrain symmetry
players per
unit
average
distance to
the opponent
the average
time opponent
comes running
m
r
d 5,13
2
1

[s]
N
,
][m
N
][ms,
rvv
d
t
539
7350
542
1
2
1
2
1






]s[3t10N 
Density of players
Ball
22 cm
68-70 cm
Pressure and jumping ball
]N[s7656,118877dspF
dsrs2A
m22,0rs
)srs2())sr(r(xA 2222




Tournaments
• there are three types of
tournaments:
- round robin tournament
- elimination tournament
- king of the hill
Round robin
tournament
Graph theory
• a branch of combinatorics which draws
heavily on geometrical ideas
• uses diagrams consisting of dots and
lines to help to get insight into a variety
of mathematical problems
B
A
C
D
Figure 1
B C
A D
P
Figure 2
B
A
C
D
First case
Second case
B C
A D
P
Elimination tournament
SemifinalFinalWinner
PAOK
Bayern
Bayern
Arsenal
PAOK
PAOK
Chelsea
Conclusion
• Maths is very
important in sports
• it can sometimes be a
reason that some team
wins
• We really need Maths
in sports!
Thanks for you
attenition!

Mathematics and sports