kojimanotech
October 29, 2018
310

# 世界一美しい数列.pdf

コジマと申します。

10/28(日)に行った社内LTでの発表用資料をアップロード用にアニメーションを省いたものです。

October 29, 2018

## Transcript

1. ੈքҰඒ͍͠਺ྻ
ίδϚ

2. ʮඒ͍͠ʯͬͯͳΜ΍
w ʮ਺ֶతʹඒ͍͠ʯ͜ͱ

3. ʮඒ͍͠ʯͬͯͳΜ΍
w ʮ਺ֶతʹඒ͍͠ʯ͜ͱ
ԫۚൺ

4. ԫۚൺͱ͸
w ͷൺ཰
1 :
1 + 5
2 (
1 + 5
2
≒ 1.618
)
w ݹ୅ΪϦγϟɺூࠁՈͷϖΠσΟΞε͕ॳΊͯ࢖ͬͨ
w ͬ͘͟Γͱ͍͏͜ͱ΋

5. ԫۚൺͷྫ
w ԫۚཐટԫۚ௕ํܗ w ϞφɾϦβ
w ϑΟϘφον਺ྻ
1,1,2,3,5,8,13,21,34,55,89,...

6. ԫۚൺͷྫ
w ԫۚཐટԫۚ௕ํܗ w ϞφɾϦβ
w ϑΟϘφον਺ྻ
1,1,2,3,5,8,13,21,34,55,89,...

7. ԫۚൺͷྫ
w ԫۚཐટԫۚ௕ํܗ w ϞφɾϦβ
w ϑΟϘφον਺ྻ
1,1,2,3,5,8,13,21,34,55,89,...
͍ͭ͜Λ
۷ΓԼ͍͛ͨ

8. ϑΟϘφον਺ྻͷ઴Խࣜ
a1
= 1,a2
= 1
an+2
= an+1
+ an
ͷͱ͖
ͱॻ͚Δ
1,1,2,3,5,8,13,21,34,55,89,...
଍͢ ଍͢
଍͢

9. ϑΟϘφον਺ྻͷҰൠ߲
w ʮϏωͷެࣜʯͱ΋ݺ͹Ε͍ͯΔ
an
=
1
5 (
1 + 5
2 )
n

(
1 − 5
2 )
n
w ূ໌͸ׂѪɻಛੑํఔࣜ࢖ͬͯূ໌Մೳ

10. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘

11. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘
Fn
=
αn+1 − βn+1
αn − βn
=
α − β (
β
α )
n
1 − (
β
α )
n

12. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘
Fn
=
αn+1 − βn+1
αn − βn
=
α − β (
β
α )
n
1 − (
β
α )
n

13. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘
Fn
=
αn+1 − βn+1
αn − βn
=
α − β (
β
α )
n
1 − (
β
α )
n
ʹऩଋ
β
α
< 1

14. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘
Fn
=
αn+1 − βn+1
αn − βn
=
α − β (
β
α )
n
1 − (
β
α )
n
n→∞
α
ʹऩଋ
β
α
< 1

15. ϑΟϘφον਺ྻͱԫۚൺͷ
ؔ܎
1 + 5
2
= α,
1 − 5
2
= β
Fn
=
an+1
an
ͱ͓͖
ͱ͓͘
Fn
=
αn+1 − βn+1
αn − βn
=
α − β (
β
α )
n
1 − (
β
α )
n
n→∞
α
ʹऩଋ
β
α
< 1
ϑΟϘφον਺ྻͷલޙͷ߲ͷൺ͸ԫۚൺʹऩଋ͢Δʂʂ

16. ࠷ޙʹϑΟϘφον਺ྻͱ͸
w લͷ߲Λ଍͠߹ΘͤͯͰ͖ΔҰݟγϯϓ
ϧͳ਺ྻ
w લޙͷ߲ͷൺ͕ԫۚൺʹऩଋ͢Δ
w ԫۚൺͱີͳؔ܎ʹ͋Δඒ͍͠਺ྻ

17. ͋Γ͕ͱ͏͍͟͝·ͨ͠ʂ