Thales’ theorem – Knowledge and References

Thales' theorem

Thales' theorem is a basic geometric theorem that extends the concepts developed with the circle to the line. It defines the equality of angles and states that the angle in a semi-circle is a right angle. It is an important theorem in a high school curriculum and is used in the construction of a right angle.From: A History of Engineering and Technology Artful Methods [2018], Exploration of polygons in a STEAM framework: technology and cultural background [2023], Geometric and Engineering Drawing [2022]

Classical Antiquity I: The Greeks

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Published in Ervan Garrison, A History of Engineering and Technology Artful Methods, 2018

Ervan Garrison

Thales had brought Egyptian geometry back to the Greek world. Thales took Egypt’s practical geometry into the abstract by development of concepts where a line becomes a directed ray. He defined the equality of angles and extended the concepts developed with the circle to the line as shown in the following examples of Thales’ Theorem of how to lay out a right angle (Figure 3.4). His theorem states that: “An angle on the circumference of a circle subtended by the diameter is always a right angle.”

Exploration of polygons in a STEAM framework: technology and cultural background

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Published in International Journal of Mathematical Education in Science and Technology, 2023

Thierry Dana-Picard, Sara Hershkovitz

A major step in the construction above was an application of Thales theorem (step e – see Figure 6), an important theorem in a high school curriculum. We assume that students, to whom this activity will be proposed, will come up with this idea; however, it is possible to perform the first steps without this theorem. Now, we will leave the grid and the coordinate axes in the screen background (we use them for step c below). Define a GeoGebra variable for φ.Plot two concentric circles with radiuses 1 and φ, respectively.Using the button , plot the angular bisectors of the axes.The points of intersection of the outer circle with the coordinate axes and the two straight lines defined in step c are the vertices of a regular octagon. The same goes for the inner circle.4 See Figure 8.From now on, act as with the previous approach.

Thales' theorem

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Classical Antiquity I: The Greeks

Exploration of polygons in a STEAM framework: technology and cultural background