Cleverly Concealed Conics Portfolio Directions: For this portfolio, you will find examples of the four conic sections in the world around you. Once you have examples of each conic section, you will choose one to analyze more closely. You will generate the equation and find the important parts of the conic section. Then you will move the foci and write a paragraph explaining the implications of the move for the application. Finally, you will reflect on your conic exploration. Be sure to complete all four parts of the portfolio before submitting to your teacher. Part 1: Conic Examples Find real-world examples of each conic section. You may find items or structures in your surroundings. You may search for items on the Internet. Complete the tables for each of your models. Provide as much detail as possible to explain how these are good examples of the conic sections. Be sure to cite your source and provide a photo or sketch. Record your notes for your example of a circular structure in the following table: Conic: Circle Notes: Example: Source: Photo or Sketch: Description of Cleverly Concealed Conic: Record your notes for your example of an elliptical structure in the following table: Conic: Ellipse Notes: Example: Source:
The Correct Answer and Explanation is:
Part 1: Conic Examples
Conic: Circle
- Notes: A circle is a conic section where all points are equidistant from a single central point. This property makes circles ideal for wheels, clocks, fountains, and domes.
- Example: Clock face on Big Ben (London)
- Source: https://www.historic-uk.com/HistoryMagazine/DestinationsUK/Big-Ben/
- Photo or Sketch:
- Description of Cleverly Concealed Conic: The face of Big Ben is a circle, cleverly designed not only for aesthetics but to ensure that time can be read accurately from any direction. Its circular design ensures the hands rotate evenly around a central pivot, maintaining constant distance and symmetry.
Conic: Ellipse
- Notes: An ellipse is a set of points where the sum of the distances from two fixed points (foci) is constant. Elliptical shapes often appear in architecture and astronomy due to their reflective properties and structural strength.
- Example: The Whispering Gallery in St. Paul’s Cathedral, London
- Source: https://www.stpauls.co.uk/history-collections/the-cathedral-buildings/the-whispering-gallery
- Photo or Sketch:
- Description of Cleverly Concealed Conic: The Whispering Gallery forms an elliptical curve. The architectural feature is cleverly concealed within the dome, but its acoustic effect — where whispers travel from one focus to another — reveals the ellipse’s mathematical nature.
Explanation
Conic sections are fundamental geometric shapes that appear subtly but powerfully in real-world design. In this portfolio, I identified a circle and an ellipse in architectural landmarks.
The circular face of Big Ben is a classic application of a circle. As all points on the clock’s face are equidistant from the center, it ensures that timekeeping hands sweep with consistent rotational motion. This perfect symmetry ensures not only aesthetic balance but also mechanical reliability. The round shape is not just decorative; it is structurally strong and allows for even distribution of stress, which is essential in large structures exposed to weather.
For the ellipse, I chose the Whispering Gallery in St. Paul’s Cathedral. Here, the elliptical shape is cleverly used to manipulate sound. In an ellipse, sound waves that start at one focus reflect off the curved walls and converge at the other focus. This design creates an acoustic marvel: a whisper spoken at one focus can be clearly heard at the other side, despite the great distance. The use of an ellipse is both functional and fascinating, showing how conic sections serve artistic, structural, and scientific purposes.
Both examples highlight how conic sections are “cleverly concealed” in the world. While they may appear as ordinary designs to the casual observer, their mathematical foundations reveal deeper functionality. Circles offer rotational symmetry and strength; ellipses provide acoustic magic and structural grace. These applications prove that conic sections are more than textbook equations—they’re essential to design, function, and experience in our daily lives.
