Problem 72 - College Algebra

Question

Consult the research department of your library or the Internet to find an example of architecture that incorporates one or more conic sections in its design. Share this example with other group members. Explain precisely how conic sections are used. Do conic sections enhance the appeal of the architecture? In what ways?

Step-by-Step Solution

Answer

The chosen example, the Gherkin building in London, employs ellipsoid shapes—which fall under conic sections—in its architectural design. This unique design provides not only an aesthetic appeal but also contributes to its structural strength.

Step 1: Understand Conic Sections

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.

Step 2: Conduct Research

Search for an example of a building or architectural feature that uses conic sections in its design. This can be a notable building, monument or other man-made structure. Some examples might include the Gherkin in London (which employs ellipsoid shapes), or the Gateway Arch in St. Louis, Missouri (which features a weighted catenary curve, a type of hyperbola).

Step 3: Analyze the Use of Conic Sections in your Chosen Example

Identify where and how conic sections are used in the design of your chosen example. For instance, the Gateway Arch in St. Louis, Missouri utilizes a weighted catenary curve—a type of hyperbola—for its unique shape, while the Gherkin building in London uses ellipsoid shapes to give it its bulbous and unique representation.

Step 4: Discuss the Appeal

Explain whether or not the use of conic sections enhances the appeal of the architecture. This will often be subjective to personal aesthetic tastes, historical and cultural significance, or its contribution to architectural innovation.