calculus

/ˈkælkjələs/ (bre, ipa) · /ˈkælkjələs/ (ame, ipa) · /ˈkal-kyə-ləs/ (ame, mw)

calculus — 名詞

1. a field of mathematics that examines how quantities vary over time, using deriva

1.名詞B2
釋義

微積分

研究連續變化的高等數學

a field of mathematics that examines how quantities vary over time, using derivatives and integrals to handle rates of change, slopes, and area

例句

Ravi struggled with differential calculus at first but later enjoyed solving rate-of-change problems.

Ravi 一開始覺得微分積分很難，但後來很喜歡解變化率的問題。

compound noun: differential calculus / integral calculus

The engineering students spent the semester learning integral calculus to compute areas under curves.

工程學系的學生花了整個學期學習積分，用來計算曲線下的面積。

文法句型

calculus

the calculus

用法筆記

Uncountable noun; often used without an article ('studying calculus') or with 'the' ('the calculus of variations'). Each subfield is named with an adjective: differential calculus, integral calculus, multivariable calculus.

常見錯誤

❌I study a calculus.
✅I study calculus.
💡Calculus is an uncountable noun and does not take 'a'.
❌Calculus are hard.
✅Calculus is hard.
💡The subject takes a singular verb even though the word ends in -s.

2. a process of carefully weighing the costs, benefits, and risks of different opti

2.名詞C1
釋義

盤算；算計

複雜情況中的利弊權衡

a process of carefully weighing the costs, benefits, and risks of different options in a complex situation before making a decision

例句

The politician's electoral calculus proved wrong when a storm shifted voter turnout in the capital.

那位政治人物的選舉盤算落空了，因為暴風雨改變了首都的投票率。

pattern: [person]'s [adjective] calculus

Leila made a quiet calculus of the risks before she accepted the hospital renovation role.

Leila 在同意領導醫院的翻新專案之前，默默盤算過各種風險。

pattern: a calculus of [noun]

同義詞
  • calculation

    more general; calculus implies a more complex, multi-factor assessment

  • reasoning

    broader; calculus emphasizes weighing trade-offs

  • assessment

    more neutral; calculus suggests strategic or political context

文法句型

a/the calculus of [something]

用法筆記

Frequently appears in the pattern 'the [person]'s calculus' or 'a/the calculus of [something]'. Common collocates include 'political', 'electoral', 'strategic', 'moral', and 'economic'.

常見錯誤

❌The calculus are too complicated to follow.
✅The calculus is too complicated to follow.
💡In this figurative sense, calculus is treated as singular or uncountable.
❌His calculus about the problem was miscalculated.
✅His calculation about the problem was wrong.
💡The figurative 'calculus' refers to the overall reasoning process, not a specific arithmetic error.

3. a hard, stone-like deposit made of mineral salts that forms inside an organ or d

3.名詞C1
釋義

結石

體內器官形成的礦物硬塊

a hard, stone-like deposit made of mineral salts that forms inside an organ or duct of the body, such as the kidneys, gallbladder, or bladder

例句

The doctor said a small calculus in Priya's kidney might pass without surgery.

醫生說 Priya 的腎臟有一顆小結石，可能不需要手術就會自行排出。

countable: a calculus / calculi (plural form)

Yusuf had two gallstones removed after an ultrasound showed the calculi blocking his bile duct.

Yusuf 取出兩顆膽結石，因為超音波顯示結石阻塞了他的膽管。

同義詞
  • stone

    common term; 'calculus' is the formal medical name

  • kidney stone

    specific to the kidneys; calculus covers all body sites

  • gallstone

    specific to the gallbladder

文法句型

a calculus

calculi (plural)

用法筆記

Countable noun; the plural form 'calculi' is standard in medical writing. Often preceded by an adjective specifying the location: 'renal calculus' (kidney), 'biliary calculus' (gallbladder), 'vesical calculus' (bladder).

常見錯誤

❌He has a lot of calculus in his kidney.
✅He has several calculi in his kidney.
💡The medical sense is countable, so use 'calculi' for multiple stones, not the uncountable 'calculus'.
❌The doctor removed the calculus from his teeth.
✅The doctor removed the kidney calculus through surgery.
💡Sense 3 refers to internal stones; dental use belongs to sense 4.

4. a hardened layer of dental plaque that builds up on the surfaces of teeth and al

4.名詞C1
釋義

牙結石

牙齒表面形成的硬質沉積

a hardened layer of dental plaque that builds up on the surfaces of teeth and along the gum line when brushing is not thorough enough

例句

The hygienist used a tool to scrape the calculus off Mei's lower front teeth during the cleaning.

牙科保健員用特殊工具刮掉 Mei 下排門牙上的牙結石。

uncountable noun: dental calculus

Regular flossing helps prevent the buildup of calculus on the back molars where a brush cannot reach easily.

定期使用牙線有助於預防後排臼齒上堆積牙結石，因為牙刷不容易刷到那裡。

collocation: buildup of calculus

同義詞
  • tartar

    common everyday term; 'calculus' is the formal dental term

  • plaque

    softer film before it hardens into calculus

文法句型

dental calculus

calculus on [teeth]

用法筆記

Uncountable noun in this sense; more commonly referred to as 'tartar' in everyday dental checkups. The phrase 'dental calculus' is the formal clinical term.

常見錯誤

❌I have a calculus on my tooth.
✅I have calculus on my teeth.
💡In the dental sense, calculus is uncountable and does not take 'a'.
❌The dentist said I have many calculi on my teeth.
✅The dentist said I have calculus buildup on my teeth.
💡Use 'calculi' only for body stones (sense 3), not for dental deposits.