1. Matemaagika
Priit Võhandu
12.09.12

2. Ilusad numbrid
11x11 = 121
111x111 = 12321
1111x1111 = 1234321
...
111111111 x 111111111 =
=12345678987654321

3. Palindroomid
• 2x819 = 9x182
3x728 = 8x273
4x217 = 7x124
• 144x441 = 252x252
156x651 = 273x372
276x672 = 384x483
• 12² = 144 ja 21² = 441
13² = 169 ja 31² = 961

4. 1089
• 732 − 237 = 495 495 + 594 = 1089
• 1 x 1089 = 1089
2 x 1089 = 2178
3 x 1089 = 3267
4 x 1089 = 4356
5 x 1089 = 5445
6 x 1089 = 6534
7 x 1089 = 7623
8 x 1089 = 8712
9 x 1089 = 9801

5. Fibonacci jada
• Jäneste paljunemine
• 1 1 2 3 5 8 13 21 34 ....

6. Fibonacci looduses

7. Kuldlõige
• Phi = 1.618033988749895…
• Phi = Fi+1 / Fi
• 1 / 1,618 = 0,618
• 1 / 0,618 = 1,618

8. Arhitektuur

9. Päikesesüsteem
Mean Relative
distance mean
Planet in million distance
kilometers where
per NASA Mercury=1
Mercury 57.91 1.00000
Venus 108.21 1.86859
Earth 149.60 1.38250
Mars 227.92 1.52353
Ceres 413.79 1.81552
Jupiter 778.57 1.88154
Saturn 1,433.53 1.84123
Uranus 2,872.46 2.00377
Neptune 4,495.06 1.56488
Pluto 5,869.66 1.30580
Total 16.18736
Average 1.61874
Phi 1.61803

10. Kunst
• Georges Pierre Seurat

11. Inimene

12. Muusika
Calculat Temper
Fibonac Musical
ed ed Note in When Octave Octave
ci Relation
Ratio
Frequen Frequen Scale
ship
A=432 * below above Meil Urmas Sisask
cy cy
1/1 440 440.00 A Root 432 216 864
Kuid arve ka
2/1 880 880.00 A Octave 864 432 1728
teisendatakse
2/3 293.33 293.66 D Fourth 288 144 576
nootideks
Aug
2/5 176 174.62 F 172.8 86.4 345.6
Fifth
3/2 660 659.26 E Fifth 648 324 1296 http://www.youtube
3/5 264 261.63 C
Minor
259.2 129.6 518.4 .com/watch?v=3174
Third
162 (Phi
T-3-59Q
3/8 165 164.82 E Fifth 81 324
)
5/2 1,100.00 1,108.72 C# Third 1080 540 2160
5/3 733.33 740.00 F# Sixth 720 360 1440
5/8 275 277.18 C# Third 270 135 540
8/3 1,173.33 1,174.64 D Fourth 1152 576 2304
Aug.
8/5 704 698.46 F 691.2 345.6 1382.4
Fifth

13. Harmooniline juhtimine
• Pascali kolmnurk

14. Harmooniline juhtimine (jätk)
• Kriitilised momendid firma kasvus, kui nii käive
kui töötajate arv kahekordistub. Milline on
hierarhia ja millised palgad?
Töötajaid Palk Töötajaid Palk
1 424 424 1 686 686
3 262 786 4 424 1696
3 162 486 6 262 1572
1 100 100 4 162 648
1 100 100
Kokku 1796 4702

15. Benfordi seadus

16. Esimese koha kontroll
3 5 ,0 0
3 0 ,0 0
2 5 ,0 0
T e g e lik%
2 0 ,0 0
O o d a ta v%
ü le m in e
1 5 ,0 0
a lu m in e
1 0 ,0 0
5 ,0 0
0 ,0 0
1 2 3 4 5 6 7 8 9

17. Kahe esimese koha kontroll
6 ,0 0
5 ,0 0
4 ,0 0
T e g e lik%
O o d a ta v%
3 ,0 0
2 ,0 0
1 ,0 0
0 ,0 0
10
17
24
31
38
45
52
59
66
73
80
87
94

18. Kahe viimase koha kontroll