calculi
calculi — 名詞
1. the plural form of calculus, referring to two or more branches of the mathematic
微積分
微分與積分的數學方法
the plural form of calculus, referring to two or more branches of the mathematical study of change — typically differential calculus (finding rates of change) and integral calculus (finding total values).
Differential and integral calculi allowed Defne to calculate the thrust needed for her model-rocket project.
微分與積分讓 Defne 能夠計算她的模型火箭所需的推力。
differential/integral calculi as paired subjects
Nora found that mastering both calculi helped her predict the orbit of the newly discovered comet.
Nora 發現掌握這兩種微積分幫助她預測了那顆新發現彗星的軌道。
Niran enrolled in vector and tensor calculi courses at ETH Zurich to prepare for relativity research.
Niran 在蘇黎世聯邦理工學院選修了向量微積分和張量微積分，為相對論研究做準備。
Before studying the two calculi, Jin completed courses in algebra and trigonometry.
在學習這兩種微積分之前，Jin 先修完了代數和三角學的課程。
Jin used differential and integral calculi to model the supply-and-demand curves in his economics project.
Jin 運用微分與積分來為他經濟學專題中的供需曲線建立模型。
- calculus
singular form; used for the subject as a whole rather than multiple branches
文法句型
calculi + of + [field]
adjective + calculi
用法筆記
This is the plural of calculus in its mathematical sense. In everyday English, calculus is uncountable ("I studied calculus"), but the plural calculi appears in academic writing when comparing two or more systems or branches.
常見錯誤
2. systems of computation or reasoning that use specially designed symbols and rule
形式系統
以符號規則推理的計算系統
systems of computation or reasoning that use specially designed symbols and rules, for example in formal logic, symbolic logic, or computer science.
Defne studied three formal calculi in her logic seminar — propositional, predicate, and temporal logic.
Defne 在邏輯研討課上學習了三種形式系統——命題邏輯、謂詞邏輯和時態邏輯。
formal calculi: systems of symbolic reasoning
Andrés compared predicate and modal calculi to see which described inference rules in legal reasoning more clearly.
Andrés 比較了謂詞邏輯與模態邏輯，看看哪一種能更清楚地描述法律推理中的推論規則。
The lambda calculus and process calculi were the two systems Soraya studied for her PhD in programming languages.
Lambda 運算與程序運算是 Soraya 攻讀程式語言博士時所研究的兩種系統。
Gita compared three modal calculi for her thesis — one for necessity, one for possibility, and one for obligation.
Gita 為她的論文比較了三種模態系統——一種處理必然性、一種處理可能性、一種處理義務。
Eric developed new temporal calculi to help an AI plan delivery routes when traffic conditions change suddenly.
Eric 開發了新的時態運算系統，幫助人工智慧在交通狀況突然改變時規劃送貨路線。
- formal systems
broader term; includes any rule-governed system, not only symbolic ones
- logical systems
more specific; refers specifically to systems of logic
文法句型
adjective + calculi
calculi of + [field]
用法筆記
Frequently paired with an adjective naming the logical domain (propositional, predicate, modal, lambda). In this sense calculi is always a count noun in the plural — the singular calculus refers to one such system.
3. hard lumps made of mineral salts that form inside hollow organs or body ducts —
結石
器官或管道中的礦物質硬塊
hard lumps made of mineral salts that form inside hollow organs or body ducts — for example, kidney stones in the urinary tract or gallstones in the gallbladder.
The X-ray showed multiple renal calculi in Padma's left kidney that required surgery.
X 光片顯示 Padma 的左腎有多顆腎結石，需要進行手術。
renal calculi: term for kidney stones
The ultrasound showed that Apinya had biliary calculi blocking bile flow from her liver, causing sharp pain in her side.
超音波檢查顯示 Apinya 的膽管結石阻塞了肝臟的膽汁流出，導致她側腹劇痛。
biliary calculi: gallstones in the bile duct
Dr. Imran removed three calculi from the ureter during the outpatient procedure.
Imran 醫師在門診手術中從輸尿管取出了三顆結石。
A diet rich in salt and low in water can increase the risk of forming urinary calculi.
高鹽飲食和水分攝取不足會增加形成泌尿結石的風險。
The ultrasound revealed small calculi in Caleb's gallbladder that required regular monitoring.
超音波檢查顯示 Caleb 的膽囊中有幾顆小結石，需要定期追蹤。
- stones
everyday word; less technical than calculi (e.g., kidney stones)
- concretions
broader medical term; includes any hardened mass, not only mineral salts
文法句型
adjective + calculi
calculi in + [body part]
plural verb
用法筆記
This is the most common context for the word calculi in medical writing. The singular form calculus ("a kidney calculus") is also used but less frequent than the plural. Common anatomical adjectives: renal (kidney), biliary (gallbladder), urinary (bladder/ureter), pancreatic (pancreas), salivary (salivary gland).
常見錯誤
4. hard, crusty deposits of mineral salts that accumulate on the surfaces of teeth,
牙結石
牙齒表面的礦物質沉積物
hard, crusty deposits of mineral salts that accumulate on the surfaces of teeth, especially near the gum line, also known as tartar.
The dental hygienist scraped away the calculi that had built up on Benjamin's molars.
牙科保健師刮掉了 Benjamin 臼齒上堆積的牙結石。
dental calculi on teeth: professional cleaning
Regular flossing helps prevent the formation of dental calculi near the gum line.
定期使用牙線有助於預防牙齦邊緣形成牙結石。
Salma's dentist said her calculi were minimal because she brushed thoroughly after every meal.
Salma 的牙醫說她因為飯後都徹底刷牙，所以牙結石很少。
Calculi on the lower front teeth are common because the salivary glands release minerals there.
下排前牙容易產生牙結石，因為唾液腺會在此處釋放礦物質。
The checkup showed no new calculi, so Nicholas only needed a standard cleaning.
檢查結果顯示 Nicholas 沒有新的牙結石，因此只需要做例行洗牙。
- tartar
common everyday term; the preferred word outside medical contexts
文法句型
dental calculi
calculi on + [teeth/gums]
用法筆記
In dentistry, the uncountable noun tartar is far more common in everyday language. Calculi is the clinical term and appears mainly in dental records, textbooks, and research papers. The singular calculus ("a deposit of dental calculus") is used when referring to the material as one mass.
常見錯誤
5. a complex framework of connected parts or principles that function together as a
複雜體系
由相互關聯的部分組成的系統
a complex framework of connected parts or principles that function together as an organized whole — often used metaphorically to describe moral, social, or political systems.
The moral calculi of different cultures can lead to very different ideas about justice and fairness.
不同文化的道德體系可能對正義與公平產生截然不同的看法。
metaphorical use: moral calculi
The intricate calculi of international trade law require years of specialised study.
錯綜複雜的國際貿易法體系需要多年的專門研究才能掌握。
Each society develops its own social calculi for weighing individual rights against the common good.
每個社會都發展出自身的社會體系，用以權衡個人權利與公共利益。
The political calculi of diplomacy shift with every change in government leadership.
外交領域的政治體系會隨著政府領導層的更迭而改變。
In rural Vietnamese villages, emotional calculi — not written contracts — decide how land is divided among adult children.
在越南鄉村，決定成年子女之間如何分配土地的，是情感體系，而不是書面契約。
- frameworks
broader; any structured set of ideas, not necessarily intricate
- systems
more general; less metaphorical than calculi
- machinery
metaphorical like calculi; suggests the moving parts of a system in operation
文法句型
the + adjective + calculi + of + [domain]
possessive + calculi
用法筆記
This sense is always metaphorical and highly formal. It typically appears with a domain adjective (moral, social, political, emotional) that names the type of system. The singular calculus is also used in the same metaphorical way (e.g., "the moral calculus of war").