幾何

See also: 几何

Chinese

Etymology

geometry: First used in Xu Guangqi and Matteo Ricci's translation of Euclid's Elements in 1607. The derivation likely comes the sense of 幾何 meaning "how many?/how much?" broadened to be a term denoting mathematics concerning number and magnitude in general. The application of the term to specifically mean geometry would have been the result of the way the work was published, in groups of books with long intervals between. When the first six books were published together, the main content of the work was on plane geometry, so 幾何 became a term referring to just that.^[1]

Pronunciation 1

		how much; how many; several how much; how many; several; a few; almost	carry; what; how carry; what; how; why; which
trad. (幾何)		幾	何
simp. (几何)		几	何

Mandarin
(Pinyin): jǐhé

(Zhuyin): ㄐㄧˇ ㄏㄜˊ
Cantonese
(Guangzhou–Hong Kong, Jyutping): gei² ho⁴

(Taishan, Wiktionary): gei² ho³
Southern Min
(Hokkien, POJ): kí-hô / kí-hô͘ / ki-hô / ki-hô͘

(Teochew, Peng'im): gi¹ ho⁵

Mandarin
- (Standard Chinese)⁺
  - Hanyu Pinyin: jǐhé
  - Zhuyin: ㄐㄧˇ ㄏㄜˊ
  - Tongyong Pinyin: jǐhé
  - Wade–Giles: chi³-ho²
  - Yale: jǐ-hé
  - Gwoyeu Romatzyh: jiiher
  - Palladius: цзихэ (czixɛ)
  - Sinological IPA ^(key): /t͡ɕi²¹⁴⁻²¹ xɤ³⁵/
- (Standard Chinese, erhua-ed)⁺
  - Hanyu Pinyin: jǐhér
  - Zhuyin: ㄐㄧˇ ㄏㄜˊㄦ
  - Tongyong Pinyin: jǐhér
  - Wade–Giles: chi³-ho²-ʼrh
  - Yale: jǐ-hér
  - Gwoyeu Romatzyh: jiiher'l
  - Palladius: цзихэр (czixɛr)
  - Sinological IPA ^(key): /t͡ɕi²¹⁴⁻²¹ xɤɻ³⁵/

Note: Erhua-ed pronunciation is only used for the geometry sense.

Cantonese
- (Standard Cantonese, Guangzhou–Hong Kong)⁺
  - Jyutping: gei² ho⁴
  - Yale: géi hòh
  - Cantonese Pinyin: gei² ho⁴
  - Guangdong Romanization: géi² ho⁴
  - Sinological IPA ^(key): /kei̯³⁵ hɔː²¹/
- (Taishanese, Taicheng)
  - Wiktionary: gei² ho³
  - Sinological IPA ^(key): /kei⁵⁵ hᵘɔ²²/
Southern Min
- (Hokkien: Xiamen, Zhangzhou, General Taiwanese)
  - Pe̍h-ōe-jī: kí-hô
  - Tâi-lô: kí-hô
  - Phofsit Daibuun: ky'hooi
  - IPA (Xiamen, Taipei): /ki⁵³⁻⁴⁴ ho²⁴/
  - IPA (Zhangzhou): /ki⁵³⁻⁴⁴ ho¹³/
  - IPA (Kaohsiung): /ki⁴¹⁻⁴⁴ hɤ²³/
- (Hokkien: Quanzhou)
  - Pe̍h-ōe-jī: kí-hô͘
  - Tâi-lô: kí-hôo
  - Phofsit Daibuun: ky'hoo
  - IPA (Quanzhou): /ki⁵⁵⁴⁻²⁴ hɔ²⁴/
- (Hokkien: Xiamen, Zhangzhou)
  - Pe̍h-ōe-jī: ki-hô
  - Tâi-lô: ki-hô
  - Phofsit Daibuun: ki'hooi
  - IPA (Xiamen): /ki⁴⁴⁻²² ho²⁴/
  - IPA (Zhangzhou): /ki⁴⁴⁻²² ho¹³/
- (Hokkien: Quanzhou)
  - Pe̍h-ōe-jī: ki-hô͘
  - Tâi-lô: ki-hôo
  - Phofsit Daibuun: ki'hoo
  - IPA (Quanzhou): /ki³³ hɔ²⁴/
- (Teochew)
  - Peng'im: gi¹ ho⁵
  - Pe̍h-ōe-jī-like: ki hô
  - Sinological IPA ^(key): /ki³³⁻²³ ho⁵⁵/

Middle Chinese: kj+jX ha

Rime
Character	幾	何
Reading #	3/4	1/2
Initial (聲)	見 (28)	匣 (33)
Final (韻)	微 (20)	歌 (94)
Tone (調)	Rising (X)	Level (Ø)
Openness (開合)	Open	Open
Division (等)	III	I
Fanqie	居狶切	胡歌切
Baxter	kj+jX	ha
Reconstructions
Zhengzhang Shangfang	/kɨi^X/	/ɦɑ/
Pan Wuyun	/kɨi^X/	/ɦɑ/
Shao Rongfen	/kiəi^X/	/ɣɑ/
Edwin Pulleyblank	/kɨj^X/	/ɦa/
Li Rong	/kiəi^X/	/ɣɑ/
Wang Li	/kĭəi^X/	/ɣɑ/
Bernhard Karlgren	/ke̯i^X/	/ɣɑ/
Expected Mandarin Reflex	jǐ	hé
Expected Cantonese Reflex	gei²	ho⁴

Old Chinese
(Baxter–Sagart): /*kəjʔ [ɡ]ˤaj/

(Zhengzhang): /*kɯlʔ ɡaːl/

Baxter–Sagart system 1.1 (2014)
Character	幾	何
Reading #	2/2	1/1
Modern Beijing (Pinyin)	jǐ	hé
Middle Chinese	‹ kjɨj^X ›	‹ ha ›
Old Chinese	/*kəjʔ/	/*[ɡ]ˁaj/
English	few; how many	what
Notes for Old Chinese notations in the Baxter–Sagart system: * Parentheses "()" indicate uncertain presence; * Square brackets "[]" indicate uncertain identity, e.g. [t] as coda may in fact be -t or -p; Angle brackets "<>" indicate infix; * Hyphen "-" indicates morpheme boundary; * Period "." indicates syllable boundary.

Zhengzhang system (2003)
Character	幾	何
Reading #	2/4	1/2
No.	5800	7458
Phonetic component	幾	可
Rime group	微	歌
Rime subdivision	1	1
Corresponding MC rime	蟣	何
Old Chinese	/*kɯlʔ/	/*ɡaːl/

Adverb

幾何

(literary) how much; how many
您女兒芳齡幾何？ [MSC, trad.]
您女儿芳龄几何？ [MSC, simp.]
Nín nǚ'ér fānglíng jǐhé? [Pinyin]
How old is your daughter? [honorific]

Synonyms

Dialectal synonyms of 多少 (“how many; how much”) [map]

Variety	Location	Words edit
Classical Chinese		幾, 幾何, 幾多, 幾許, 多少
Formal (Written Standard Chinese)		多少
Northeastern Mandarin	Beijing	多少
	Taiwan	多少
	Singapore	多少
Jilu Mandarin	Jinan	多少
Central Plains Mandarin	Xi'an	多少
Southwestern Mandarin	Chengdu	好多
	Wuhan	幾多, 好多
	Guilin	好多
	Xiangtan (Jiangnan Industries Group koine)	幾, 幾多
Jianghuai Mandarin	Yangzhou	多少
Jianghuai Mandarin	Hefei	好些, 好多
Cantonese	Guangzhou	幾多, 幾
	Hong Kong	幾多, 幾
	Taishan	幾多
	Dongguan	幾多
	Yangjiang	幾多, 幾
	Singapore (Guangfu)	幾多, 幾
Gan	Nanchang	幾多
Hakka	Meixian	幾多
	Miaoli (N. Sixian)	幾多
	Pingtung (Neipu; S. Sixian)	幾多
	Hsinchu County (Zhudong; Hailu)	幾多
	Taichung (Dongshi; Dabu)	幾多
	Hsinchu County (Qionglin; Raoping)	幾多
	Yunlin (Lunbei; Zhao'an)	幾多
Jin	Taiyuan	多少
Northern Min	Jian'ou	幾多
Eastern Min	Fuzhou	若夥
Eastern Min	Singapore (Fuqing)	若夥
Southern Min	Xiamen	偌濟
	Quanzhou	偌濟
	Shishi	偌濟
	Zhangzhou	偌濟
	Zhao'an	偌濟
	Tainan	偌濟, 幾
	Penang (Hokkien)	幾
	Singapore (Hokkien)	偌濟, 幾
	Manila (Hokkien)	偌濟, 幾
	Chaozhou	若濟
	Shantou	若濟
	Jieyang	若濟
	Puning	若濟
	Pontianak (Teochew)	若濟
	Haikou	偌濟
Southern Pinghua	Nanning (Tingzi)	幾多
Wu	Shanghai	多少, 幾化, 幾多化 dated
	Shanghai (Qingpu)	幾好
	Shanghai (Jiading)	幾漢
	Shanghai (Chongming)	多話
	Suzhou	幾化
	Wuxi	幾化
	Ningbo	多少
	Wenzhou	幾倈兒, 幾倈
	Lishui	幾粒
	Qingyuan	多
Xiang	Changsha	好多
	Xiangtan	幾, 幾多
	Shuangfeng	好多, 幾多

Derived terms

Noun

幾何

(mathematics) geometry [from 1607]

Derived terms

代數幾何 / 代数几何 (dàishù jǐhé)
平面幾何 / 平面几何 (píngmiàn jǐhé)
幾何光學 / 几何光学 (jǐhé guāngxué)
幾何圖形 / 几何图形 (jǐhé túxíng)
幾何學 / 几何学 (jǐhéxué)
幾何級數 / 几何级数 (jǐhé jíshù)
幾何體 / 几何体 (jǐhétǐ)
微分幾何 / 微分几何 (wēifēn jǐhé)
立體幾何 / 立体几何 (lìtǐ jǐhé)
解析幾何 / 解析几何 (jiěxī jǐhé)

Descendants

Sino-Xenic (幾何):

→ Japanese: 幾何(きか) (kika)
→ Korean: 기하(幾何) (giha)
→ Vietnamese: kỉ hà (幾何)

Pronunciation 2

	how much; how many; several how much; how many; several; a few; almost	carry; what; how carry; what; how; why; which
trad. (幾何)	幾	何
simp. (几何)	几	何
alternative forms	幾好／几好

Cantonese (Taishan, Wiktionary): gei² hau^4*

Cantonese
- (Taishanese, Taicheng)
  - Wiktionary: gei² hau^4*
  - Sinological IPA ^(key): /kei⁵⁵ hau²¹⁻²¹⁵/

Adverb

幾何

(Taishanese) how
(Taishanese) why

Synonyms

Dialectal synonyms of 怎樣 (“how”) [map]

Variety	Location	Words edit
Classical Chinese		如何, 何以, 若何
Formal (Written Standard Chinese)		如何, 怎樣
Northeastern Mandarin	Beijing	怎麼樣兒, 怎樣兒
	Taiwan	怎麼樣, 怎樣, 如何
	Malaysia	怎麼樣, 怎樣, 如何
	Singapore	怎麼樣, 怎樣, 如何
Jilu Mandarin	Jinan	怎麼樣
Central Plains Mandarin	Xi'an	咋樣兒
Southwestern Mandarin	Chengdu	咋個樣, 咋個樣子, 啷個樣, 啷個樣子
	Wuhan	麼樣, 麼樣子, 哪樣, 哪樣子
	Guilin	啷子樣
Jianghuai Mandarin	Yangzhou	怎們樣, 哪一個樣, 哪一個樣子
Jianghuai Mandarin	Hefei	怎樣
Cantonese	Guangzhou	點樣, 點
	Hong Kong	點樣, 點
	Hong Kong (Kam Tin; Weitou)	點樣
	Macau	點樣, 點
	Guangzhou (Panyu)	點
	Guangzhou (Zengcheng)	點樣, 點樣做
	Foshan	點
	Foshan (Shatou, Nanhai)	點
	Foshan (Shunde)	點, 點樣
	Foshan (Sanshui)	點
	Foshan (Mingcheng, Gaoming)	點
	Zhongshan (Shiqi)	點子
	Zhongshan (Huancheng)	點子
	Zhongshan (Nanlang)	點子
	Zhongshan (Xiaolan)	點
	Zhongshan (Dongsheng, Xiaolan)	點, 點樣
	Zhongshan (Tanbei, Xiaolan)	點, 點樣
	Zhongshan (Henglan)	點, 點樣
	Zhongshan (Dongfeng)	點, 點樣
	Zhongshan (Nantou)	點, 點樣
	Zhongshan (Fusha)	點, 點樣
	Zhongshan (Shalang)	點, 點樣
	Zhongshan (Gangkou)	點, 點樣
	Zhongshan (Huangpu)	點, 點樣
	Zhongshan (Langwang, Minzhong)	點, 點樣
	Zhongshan (Minzhong)	點, 點樣
	Zhongshan (Banfu)	點, 點樣
	Zhongshan (Tanzhou)	點, 點樣
	Zhuhai (Qianshan, Xiangzhou)	點樣
	Zhuhai (Shangheng, Doumen; Tanka)	點
	Zhuhai (Doumen)	點
	Taishan	幾何
	Singapore (Guangfu)	點樣, 點
Gan	Nanchang	啷樣, 啷
Hakka	Meixian	仰般, 仰仔
	Miaoli (N. Sixian)	仰般, 仰仔
	Pingtung (Neipu; S. Sixian)	仰仔
	Hsinchu County (Zhudong; Hailu)	仰般
	Taichung (Dongshi; Dabu)	仰脣, 仰
	Hsinchu County (Qionglin; Raoping)	仰般, 仰般形
	Yunlin (Lunbei; Zhao'an)	仰子
Jin	Taiyuan	咋, 咋底
Northern Min	Jian'ou	何如, 何如事
Eastern Min	Fuzhou	將樣, 蔣樣, 蔣其
Southern Min	Xiamen	按怎, 怎樣, 啥款
	Quanzhou	障仔, 怎樣, 按怎, 啥款
	Zhangzhou	按怎, 怎樣, 啥款
	Tainan	按怎, 怎仔樣, 怎樣仔, 啥款
	Penang (Hokkien)	按怎
	Singapore (Hokkien)	按怎
	Manila (Hokkien)	障仔, 怎樣
	Chaozhou	在生樣, 乜生樣, 做呢
	Shantou	在生
	Jieyang	在生, 在生樣
	Haifeng	做呢, 做呢樣
	Singapore (Teochew)	做呢, 在生
Zhongshan Min	Zhongshan (Longdu, Shaxi)	哪, 哪樣
Wu	Shanghai	哪能, 哪能介, 哪能樣子
	Suzhou	捺亨
	Wenzhou	訾那, 訾那能
Xiang	Changsha	何是, 何裡
Xiang	Shuangfeng	麼家

Dialectal synonyms of 為什麼 (“why”) [map]

Variety	Location	Words edit
Classical Chinese		何為, 何以, 何, 何故, 緣何, 胡, 奚, 曷, 胡為
Formal (Written Standard Chinese)		為什麼, 為何, 因何, 何以
Northeastern Mandarin	Beijing	為什麼, 幹嗎, 幹什麼
	Taiwan	為什麼
	Harbin	為啥
	Malaysia	為什麼, 做什麼, 做麼
	Singapore	為什麼, 做什麼, 做麼
Jilu Mandarin	Tianjin	為嘛
Jilu Mandarin	Jinan	為麼兒, 為麼, 幹麼兒, 為什麼
Jiaoliao Mandarin	Yantai (Muping)	為麼, 為麼個
Central Plains Mandarin	Xi'an	為啥, 因啥
	Xining	為啥
	Xuzhou	為啥, 擁啥, 擁什麼
Lanyin Mandarin	Yinchuan	為啥
	Lanzhou	為啥
	Ürümqi	為啥
Southwestern Mandarin	Chengdu	為啥子, 做啥子
	Wuhan	做麼事, 為麼事
	Guiyang	為哪樣, 為些哪樣
	Guilin	為什麼
	Liuzhou	為什麼
	Xiangtan (Jiangnan Industries Group koine)	為什麼
Jianghuai Mandarin	Nanjing	為什麼
	Yangzhou	甚們事, 做事, 做啥, 為甚們 formal
	Hefei	怎搞, 怎搞的
Cantonese	Guangzhou	點解, 做乜, 做乜嘢, 為乜, 為乜為物, 做乜事幹, 因乜事幹, 因乜解究, 因乜緣故, 何解, 乜, 咩
	Hong Kong	點解, 做乜, 做乜嘢, 做咩, 為乜, 為咩, 做乜事幹, 因乜事幹, 因乜解究, 因咩解究, 因乜緣故, 何解, 乜, 咩
	Hong Kong (Kam Tin; Weitou)	做乜嘢
	Macau	為乜嘢
	Guangzhou (Panyu)	點解
	Guangzhou (Huashan, Huadu)	整乜嘢
	Guangzhou (Zengcheng)	做乜嘢
	Foshan	點解
	Foshan (Shatou, Nanhai)	點解
	Foshan (Shunde)	為乜嘢
	Foshan (Mingcheng, Gaoming)	因乜嘢, 點解
	Zhongshan (Shiqi)	為乜嘢
	Zhuhai (Qianshan, Xiangzhou)	為乜嘢
	Zhuhai (Shangheng, Doumen; Tanka)	點解
	Zhuhai (Doumen)	點解
	Jiangmen (Baisha)	點解
	Taishan	幾何, 幾解, 做乜, 為乜, 乜頭路
	Kaiping (Chikan)	幾解
	Enping (Niujiang)	做乜
	Dongguan	點解, 做乜嘢, 做乜, 為乜嘢
	Shenzhen (Shajing, Bao'an)	點解
	Shenzhen (Dapeng)	點解
	Yangjiang	為乜, 為乜事, 做乜, 做乜事, 做乜嘢
	Hepu (Lianzhou)	為物底
	Qinzhou	為乜嘢, 為乜
	Qinzhou (Xiniujiao)	為乜底
	Beihai	為乜嘢
	Beihai (Nankang)	做乜嘢
	Beihai (Yingpan)	為乜底
	Beihai (Qiaogang - Cô Tô)	做乜嘢, 為乜
	Beihai (Qiaogang - Cát Bà)	做乜嘢
	Fangchenggang (Fangcheng)	做乜嘢, 為乜
	Kuala Lumpur (Guangfu)	點解
	Singapore (Guangfu)	點解
	Ho Chi Minh City (Guangfu)	做乜嘢
	Móng Cái	點解, 為乜
	Yangon (Taishan)	幾解
Gan	Nanchang	為什哩
Gan	Pingxiang	為咋個, 為咋哩, 做咋個, 做咋哩, 何解
Hakka	Meixian	做麼個
	Huizhou (Huicheng; Bendihua)	做乜嘢, 做嘢
	Dongguan (Qingxi)	做麼個
	Shenzhen (Shatoujiao)	做麼個
	Zhongshan (Wuguishan)	仰解, 做乜嘢
	Zhongshan (Nanlang Heshui)	為乜嘢
	Guangzhou (Lütian, Conghua)	為麼個
	Miaoli (N. Sixian)	做麼個
	Pingtung (Neipu; S. Sixian)	做麼個
	Hsinchu County (Zhudong; Hailu)	做麼個
	Taichung (Dongshi; Dabu)	做麼個
	Hsinchu County (Qionglin; Raoping)	做麼個
	Yunlin (Lunbei; Zhao'an)	做麼個
	Hong Kong	做麼個
	Kuching (Hepo)	做乜個
Jin	Taiyuan	為甚, 因為甚, 幹什
Jin	Xinzhou	𠰻們
Northern Min	Jian'ou	為孰事, 做孰事
Eastern Min	Fuzhou	蔣其, 蔣講, 做什乇, 做什名, 幹乜勢, 傒勢
	Fuzhou (Changle)	傒勢
	Fuqing	介計
	Yongtai	蔣其
	Gutian	做什乇
	Fu'an	做乜乇
	Ningde	做乇
	Shouning	做呢乇
	Zhouning	做乜乇
	Fuding	做哪乇
	Matsu	為什乇, 蔣其, 蔣講, 做什乇, 傒勢
Southern Min	Xiamen	為什物, 按怎, 物代, 敢咧, 創什物
	Quanzhou	按怎, 物代
	Jinjiang	為啥物
	Zhangzhou	按怎
	Zhao'an	為甚物
	Dongshan	為甚物
	Taipei	為啥物, 是按怎
	Penang (Hokkien)	何物事, 做物事, 做物
	Singapore (Hokkien)	按怎
	Manila (Hokkien)	敢哪, 敢哪誌
	Chaozhou	做呢
	Shantou	做呢
	Shantou (Chaoyang)	做呢
	Singapore (Teochew)	做呢
	Leizhou	作乜, 因乜
	Wenchang	作乜, 因乜, 怎作
	Haikou	作乜, 作個乜, 作乜物, 因乜, 因個乜
	Singapore (Hainanese)	作乜
Zhongshan Min	Zhongshan (Longdu, Shaxi)	為乜嘢
Southern Pinghua	Nanning (Tingzi)	做門, 做哪門, 為哪門
Waxiang	Guzhang (Gaofeng)	為什個
Wu	Shanghai	啥體, 為啥, 做啥, 啥講究, 為啥體, 啥個講究, 啥道理, 為啥道理, 啥個路道, 啥個緣故
	Shanghai (Chongming)	為何, 做何
	Suzhou	為啥, 為點啥, 做啥, 啥體, 為啥體
	Danyang	為點高, 做點高
	Hangzhou	為啥
	Wenzhou	妝乜, 為何呢, 為乜事幹
	Jinhua	為淡事幹, 為待西
Xiang	Changsha	為麼子, 何解
	Xiangtan	奚解
	Loudi	嗎介
	Shuangfeng	為麼子, 做麼子

Japanese

Etymology 1

Kanji in this term
幾	何
き Grade: S	か Grade: 2
kan'on

Shortening of 幾何学 (kikagaku, “geometry”).^[2]^[3]

First attested in the early Meiji period, in a text from 1886.^[2]

Pronunciation

(Tokyo) きか [kíꜜkà] (Atamadaka – [1])^[3]
(Tokyo) きか [kìkáꜜ] (Odaka – [2])^[3]
IPA^(key): [kʲika̠]

Noun

幾(き)何(か) • (kika)

[1886] (mathematics, colloquial) Short for 幾何学 (kikagaku): geometry

Derived terms

幾(き)何(か)異(い)性(せい) (kika isei)
幾(き)何(か)画(が)法(ほう) (kika gahō)
幾(き)何(か)級(きゅう)数(すう) (kika kyūsū, “geometric series, geometric progression”)
幾(き)何(か)原(げん)本(ぽん) (Kika Genpon)
幾(き)何(か)光(こう)学(がく) (kikakōgaku)
幾(き)何(か)公(こう)理(り) (kika kōri)
幾(き)何(か)数(すう)列(れつ) (kika sūretsu)
幾(き)何(か)中(ちゅう)項(こう) (kika chūkō)
幾(き)何(か)平(へい)均(きん) (kika heikin)
幾(き)何(か)模(も)様(よう) (kika moyō)
位(い)相(そう)幾(き)何(か) (isō kika, “topology”)
代(だい)数(すう)幾(き)何(か) (daisū kika, “algebraic geometry”)
直(ちょっ)観(かん)幾(き)何(か) (chokkan kika)
微(び)分(ぶん)幾(き)何(か) (bibun kika, “differential geometry”)
ユークリッド幾(き)何(か) (Yūkuriddo kika, “Euclidean geometry”)
リーマン幾(き)何(か) (Rīman kika, “Riemannian geometry”)
論(ろん)証(しょう)幾(き)何(か) (ronshō kika)

Etymology 2

Kanji in this term
幾	何
いく Grade: S	ばく Grade: 2
kun'yomi	irregular

For pronunciation and definitions of 幾何 – see the following entry.

【幾許いくばく】	[adverb] how much, how many [adverb] (usually followed by か (ka)), few, a little bit [adverb] (chiefly in the negative) a little bit, not much Alternative spelling 幾ばく
【幾許こきし】	[adverb] many, a lot Alternative spellings 幾ばく, こきだ, ここだ, ここば, ここら
【幾許いくだ】	[adverb] (chiefly in the negative) a little bit, not much Alternative spelling 幾ばく

(This term, 幾何, is an alternative spelling of the above term.)

Usage notes

The kanji spelling is an orthographic borrowing from Chinese 幾何 / 几何 (jǐhé).

References

^ [https://www.gcoe.lit.nagoya-u.ac.jp/result/pdf/5-1_%E5%B0%8F%E5%B7%9D(E).pdf

Vietnamese

chữ Hán Nôm in this term
幾	何

Adjective

幾何

chữ Hán form of kỉ hà (“geometric”).

[1] [https://www.gcoe.lit.nagoya-u.ac.jp/result/pdf/5-1_%E5%B0%8F%E5%B7%9D(E).pdf

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[2]

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