The use of threads and nails in geometry

52 Views Asked by At

For a long time, I have been thinking about starting to study geometry that uses strings and nails, but I was postponing the idea. In fact, strings and nails are more advanced tools than a ruler and a compass, and they enable us to perform many additional constructions that are not possible to do with a ruler and a compass.

I do not claim to be the discoverer of these tools, it is widely known how to create conic sections using threads and nails, but I am really upset by the great neglect of these wonderful tools, in fact they are capable of creating more sophisticated curves than conic sections.

Perhaps the main obstacle behind using threads and nails in engineering is the lack of familiarity with the possible ways of using them. It is very loose. I will only suggest a few possible ways of using them. I hope that the engineering of these tools will be developed over time, and I will certainly provide some answers in the future.

  1. You have an unlimited supply of string, nails, and endless ink to draw whatever you want.
  2. If you have two nails, you can attach the two taut ends of the thread to the two nails to draw a straight line connecting them through the taut thread.
  3. For a fixed nail, you can tie the string to one side, choose an optional length, tie the pen to the other side, and draw a circle with the center of the fixed nail and its radius being the length you chose.
  4. You are allowed to set the intersection point of two strings or the intersection point of two shapes drawn using the strings.
  5. You are allowed to install a nail in the position of a drawn point.
  6. It is permissible to tighten the thread at two set screws or two marked points and cut it to this length.
  7. It is permissible to install two nails on the ground, tie a string longer than the distance between them, and then draw an ellipse by keeping the string taut with a pen.
  8. It is permissible to make knots using threads at intersection points, drawn points, and nails. Thus, a complete structure can be made of threads and moved, which will have greater freedom of movement than simply pulling out.
  9. It is permissible to rely on the tension constraints of two threads at the same time to determine the intersection point of the two tensioned threads.
  10. There are greater possibilities than what have been proposed, perhaps classified with a more permissive geometry in terms of tools, for example the possibility of bending the thread to make it into a drawn curve and then freezing it, or the use of rubber threads that maintain the proportions of the points set on them, or the possibility of connecting the threads via retractable knots on the Threads and other capabilities.

I assert that threads and nails provide much more sophisticated construction than may seem and therefore more importance should be given to their study.

This question is broad in terms of what can be provided in answers. Here are some suggestions:

  1. Pointing out other ways to use threads and nails in engineering construction.
  2. Pointing out curves that can be created using threads and screws.
  3. Reference to previous research or known constructions that use threads and nails.