Short Ruler Construction of a Mid Point/ Perpendicular Bisector of a Line Segment

In this video, Chris Tisdell continues his series on geometry and geometric constructions, focusing on how to perform constructions using a straight edge of limited length. He introduces the idea that ancient Greek geometry assumptions, taught in schools, involve drawing circles of any size and joining any two points, which doesn't necessarily correspond to reality where rulers and straight edges are finite in length.

Chris uses a tool that includes a circle arc template and a straight edge marked with points P and R. He explains that the length of the straight edge is the same as the radius of the circle arc template.

The main construction demonstrated in the video is how to bisect a given line segment, in this case, a line segment AB.Chris begins by using the circle arc template to create two points, C and D, on the line segment AB. The tool allows him to measure the distances accurately. 

Next, Chris constructs a triangle CED, where CD is the base and CE is one of the legs. He then constructs a parallel line, KJ, to AB, passing through point E.

To ensure that the lengths remain within the capability of the limited-length straight edge, Chris uses construction techniques like creating rhombuses and utilising the circle arc template to extend lines.

Once the parallel line KJ is established,Chris finds the diagonals of the trapezoid formed by the lines CD and GJ. The diagonals intersect at a point closer to E, which is labeled as L.

Finally, Chris connects point E to L, and the resulting line segment EM serves as the perpendicular bisector of line segment AB. This construction effectively divides AB into two equal halves, demonstrating a workaround for performing geometric constructions with a limited-length straight edge.

Chris emphasises the creativity required to overcome the challenge of working with finite tools and highlights the benefits of thinking differently when approaching geometric problems.

Overall, the video provides a practical example of how to perform geometric constructions using a finite straight edge and a circle arc template, offering an insightful perspective on the subject of geometry.