cotangency
Cotangency is a geometric property describing the state of two curves or surfaces that touch each other at a single point and share a common tangent line or plane at that point. It implies that the slopes or derivatives of the curves are identical at the point of contact without the curves necessarily crossing one another.
Examples
3 of 5The artist carefully positioned the two spheres to highlight their point of cotangency.
The artist carefully positioned the two spheres to highlight their point of cotangency.
In advanced calculus, the cotangency of these two functions must be proven before proceeding with the theorem.
In advanced calculus, the cotangency of these two functions must be proven before proceeding with the theorem.
If you look at where the tires meet the road, you can see the cotangency in action.
If you look at where the tires meet the road, you can see the cotangency in action.
Synonyms
Antonyms
Word Family
Memory Tip
Remember 'Co-' (together) and 'tangent' (touching); cotangency is when two things touch together perfectly at one point.
Quick Quiz
The engineer checked the ________ of the two pipes to ensure there was no overlap in the blueprint.
Correct!
The correct answer is: cotangency
Examples
The artist carefully positioned the two spheres to highlight their point of cotangency.
everydayThe artist carefully positioned the two spheres to highlight their point of cotangency.
In advanced calculus, the cotangency of these two functions must be proven before proceeding with the theorem.
formalIn advanced calculus, the cotangency of these two functions must be proven before proceeding with the theorem.
If you look at where the tires meet the road, you can see the cotangency in action.
informalIf you look at where the tires meet the road, you can see the cotangency in action.
The researcher focused on the cotangency conditions of non-linear manifolds within a multi-dimensional space.
academicThe researcher focused on the cotangency conditions of non-linear manifolds within a multi-dimensional space.
We need to ensure the cotangency of our supply chains to prevent any gaps in the manufacturing process.
businessWe need to ensure the cotangency of our supply chains to prevent any gaps in the manufacturing process.
Synonyms
Antonyms
Word Family
Common Collocations
Common Phrases
at the point of cotangency
at the exact location where the lines touch
cotangency relation
the mathematical relationship between two tangent entities
cotangency theorem
a formal rule regarding tangent points
Often Confused With
Cotangent is a specific trigonometric ratio (1/tan), while cotangency is the state of being tangent.
Usage Notes
Cotangency is primarily used in mathematical, architectural, and engineering contexts to describe the precise alignment of shapes. In business or general English, it is used metaphorically to describe things that align or touch without overlapping.
Common Mistakes
Learners often use the word 'cotangent' (the adjective/trig function) when they mean 'cotangency' (the noun describing the state).
Memory Tip
Remember 'Co-' (together) and 'tangent' (touching); cotangency is when two things touch together perfectly at one point.
Word Origin
Derived from the Latin 'co-' (together) and 'tangere' (to touch).
Grammar Patterns
Quick Quiz
The engineer checked the ________ of the two pipes to ensure there was no overlap in the blueprint.
Correct!
The correct answer is: cotangency
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