Asymptotic developable – Definition & Meaning

Asymptotic developable is a term that is often used in mathematics and engineering. It refers to a surface that can be flattened into a plane without distorting its shape or changing its area. In this article, we will explore the definition and meaning of asymptotic developable, its origin, and its associations.

Definitions

An asymptotic developable is a surface that can be flattened into a plane without stretching or tearing. It is a surface that has two asymptotic lines that intersect at each point on the surface. These lines are called the principal directions of the surface. An asymptotic developable is also known as a ruled surface, as it can be generated by a straight line moving along a curve.

Origin

The term asymptotic developable was first used by the French mathematician Jean Baptiste Meusnier in the late 18th century. Meusnier was interested in the geometry of surfaces and was the first to study the properties of asymptotic lines on surfaces.

Meaning in different dictionaries

According to the Oxford English Dictionary, asymptotic developable is defined as “a surface that can be flattened into a plane without stretching or tearing.” The Merriam-Webster Dictionary defines it as “a surface that can be developed without stretching or tearing.”

Associations

Asymptotic developable surfaces are often used in engineering and architecture to create curved structures that can be flattened into two-dimensional plans. They are also used in the design of aircraft wings and other aerodynamic surfaces.

Synonyms

Some synonyms of asymptotic developable include ruled surface, developable surface, and unrolled surface.

Antonyms

Antonyms of asymptotic developable include non-developable surface, non-ruled surface, and non-flattenable surface.

The same root words

The term asymptotic comes from the Greek word asymptotos, which means “not falling together.” Developable comes from the Latin word developpare, which means “to unroll.”

Example Sentences

1. The wings of the airplane were designed using an asymptotic developable surface to maximize aerodynamic efficiency.
2. The architect used an asymptotic developable surface to create the curved roof of the building.
3. The engineer used a computer program to generate an asymptotic developable surface for the design of the car body.