Batang pembilang: Perbezaan antara semakan
Kandungan dihapus Kandungan ditambah
Orhanghazi (bincang | sumb.) |
Orhanghazi (bincang | sumb.) Tiada ringkasan suntingan |
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Baris 174:
| style="width:50px" | [[File:Counting rod h2.png]]
| style="width:50px" |
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== Angka batang ==
Angka batang ialah satu sistem angka bertatatanda kedudukan yang dibina berdasarkan bentuk batang pembilang. Dalam sistem ini, nombor positif ditulis seperti biasa dan nombor negatif ditanda dengan palang condong pada digit terakhir.
Satu bulatan (〇) digunakan untuk 0. Ramai ahli sejarah menganggap ia diimport dari [[angka India]] oleh [[Gautama Siddha]] pada tahun 718<ref name="wang"/>, namun ada juga yang mengatakan ia dicipta dari pengisi ruang teks Cina "□"<ref name="qian">{{ Citation
| title=Zhongguo Shuxue Shi (The history of Chinese mathematics)
| last=Qian
| first=Baocong
| year=1964
| publisher=Kexue Chubanshe
| place=Beijing
}}</ref>.
Pada abad ke-13, ahli matematik [[dinasti Song|Song selatan]] telah mengubah digit untuk 4,5, dan 9 bagi mengurangkan lejang aksara<ref name="qian"/>. Bentuk melintang yang baru secara beransur-ansur berubah menjadi [[angka Suzhou]]. Bagaimanapun, orang Jepun terus kekal menggunakan bentuk tradisionalnya.
{| class="wikitable" border="1" style="text-align:center"
|+ Nombor positif (tradisional)
|-
!
! style="width:50px" | 0
! style="width:50px" | 1
! style="width:50px" | 2
! style="width:50px" | 3
! style="width:50px" | 4
! style="width:50px" | 5
! style="width:50px" | 6
! style="width:50px" | 7
! style="width:50px" | 8
! style="width:50px" | 9
|-
! style="height:50px" | Menegak
| [[File:Counting rod 0.png]]
| [[File:Counting rod v1.png]]
| [[File:Counting rod v2.png]]
| [[File:Counting rod v3.png]]
| [[File:Counting rod v4.png]]
| [[File:Counting rod v5.png]]
| [[File:Counting rod v6.png]]
| [[File:Counting rod v7.png]]
| [[File:Counting rod v8.png]]
| [[File:Counting rod v9.png]]
|-
! style="height:50px" | Melintang
| [[File:Counting rod 0.png]]
| [[File:Counting rod h1.png]]
| [[File:Counting rod h2.png]]
| [[File:Counting rod h3.png]]
| [[File:Counting rod h4.png]]
| [[File:Counting rod h5.png]]
| [[File:Counting rod h6.png]]
| [[File:Counting rod h7 num.png]]
| [[File:Counting rod h8 num.png]]
| [[File:Counting rod h9 num.png]]
|}
{| class="wikitable" border="1" style="text-align:center"
|+ Nombor negatif (tradisional)
|-
!
! style="width:50px" | -0
! style="width:50px" | -1
! style="width:50px" | -2
! style="width:50px" | -3
! style="width:50px" | -4
! style="width:50px" | -5
! style="width:50px" | -6
! style="width:50px" | -7
! style="width:50px" | -8
! style="width:50px" | -9
|-
! style="height:50px" | Menegak
| [[File:Counting rod -0.png]]
| [[File:Counting rod v-1.png]]
| [[File:Counting rod v-2.png]]
| [[File:Counting rod v-3.png]]
| [[File:Counting rod v-4.png]]
| [[File:Counting rod v-5.png]]
| [[File:Counting rod v-6.png]]
| [[File:Counting rod v-7.png]]
| [[File:Counting rod v-8.png]]
| [[File:Counting rod v-9.png]]
|}
{| class="wikitable" border="1" style="text-align:center"
|+ Nombor positif (Song selatan)
|-
!
! style="width:50px" | 0
! style="width:50px" | 1
! style="width:50px" | 2
! style="width:50px" | 3
! style="width:50px" | 4
! style="width:50px" | 5
! style="width:50px" | 6
! style="width:50px" | 7
! style="width:50px" | 8
! style="width:50px" | 9
|-
! style="height:50px" | Menegak
| [[File:Counting rod 0.png]]
| [[File:Counting rod v1.png]]
| [[File:Counting rod v2.png]]
| [[File:Counting rod v3.png]]
| [[File:Counting rod 4 song.png]]
| [[File:Counting rod v5 song.png]]
| [[File:Counting rod v6.png]]
| [[File:Counting rod v7.png]]
| [[File:Counting rod v8.png]]
| [[File:Counting rod v9 song.png]]
|-
! style="height:50px" | Melintang
| [[File:Counting rod 0.png]]
| [[File:Counting rod h1.png]]
| [[File:Counting rod h2.png]]
| [[File:Counting rod h3.png]]
| [[File:Counting rod 4 song.png]]
| [[File:Counting rod h5 song.png]]
| [[File:Counting rod h6.png]]
| [[File:Counting rod h7 num.png]]
| [[File:Counting rod h8 num.png]]
| [[File:Counting rod h9 song.png]]
|}
Contoh:
{| class="wikitable" border="1" style="text-align:center"
! !! Tradisional !! Song selatan
|-
! style="text-align:right;height:50px" | 231
| [[File:Counting rod v2.png]][[File:Counting rod h3.png]][[File:Counting rod v1.png]]
| [[File:Counting rod v2.png]][[File:Counting rod h3.png]][[File:Counting rod v1.png]]
|-
! style="text-align:right;height:50px" | 5089
| [[File:Counting rod h5.png]][[File:Counting rod 0.png]][[File:Counting rod h8 num.png]][[File:Counting rod v9.png]]
| [[File:Counting rod h5 song.png]][[File:Counting rod 0.png]][[File:Counting rod h8 num.png]][[File:Counting rod v9 song.png]]
|-
! style="text-align:right;height:50px" | -407
| [[File:Counting rod v4.png]][[File:Counting rod 0.png]][[File:Counting rod v-7.png]]
| [[File:Counting rod 4 song.png]][[File:Counting rod 0.png]][[File:Counting rod v-7.png]]
|-
! style="text-align:right;height:50px" | -6720
| [[File:Counting rod h6.png]][[File:Counting rod v7.png]][[File:Counting rod h2.png]][[File:Counting rod -0.png]]
| [[File:Counting rod h6.png]][[File:Counting rod v7.png]][[File:Counting rod h2.png]][[File:Counting rod -0.png]]
|}
Di Jepun, [[Seki Takakazu]] telah membangunkan angka batang menjadi tatatanda simbolik untuk algebra dan secara drastik menambah baik [[matematik Jepun]].<ref name="wang"/> Selepas era ini, sistem angka tatatanda kedudukan yang menggunakan karakter [[angka Cina]] telah dicipta, manakala angka batang hanya digunakan sebagai tanda tambah dan tolak.
{| class="wikitable" border="1" style="text-align:center"
! Barat!! Seki !! Selepas Seki
|-
| ''x'' + ''y'' + 246
| <big>'''[[File:Counting rod v1.png]]甲[[File:Counting rod v1.png]]乙[[File:Counting rod v2.png]][[File:Counting rod h4.png]][[File:Counting rod v6.png]]
| <big>'''[[File:Counting rod v1.png]]甲[[File:Counting rod v1.png]]乙[[File:Counting rod v1.png]]二四六
|-
| 5''x'' - 6''y''
| <big>'''[[File:Counting rod v5.png]]甲[[File:Counting rod v-6.png]]乙
| <big>'''[[File:Counting rod v1.png]]五甲[[File:Counting rod v-1.png]]六乙
|-
| 7''xy''
| <big>'''[[File:Counting rod v7.png]]甲乙 d
| <big>'''[[File:Counting rod v1.png]]七甲乙
|-
| 8''x'' / ''y''
| N/A
| <big>'''乙[[File:Counting rod v1.png]]八甲</big>'''
|}
| |||