The Lune of Hippocrates:
... Further Fascinating Relationships

by

 Markus Heisss

 Würzburg, Bavaria

  08/2023 (Last update: August 27, 2023)

    The copying of the following graphics is allowed, but without changes.

[To get a bigger picture, please click it with the cursor.]

The important information you'll find in the graphics.

 

 

Let's start with a drawing, showing a relationship which should be clear:

Hippocrates, curved triangle, squaring
Fig.01: Constructive Quadrature of a Lune Segment

If this relationship ISN'T kwown yet, I recommend to study a website

which has all important basics to the lunes of Hippocrates: [here]

 

The following figure contains all important information for the next step:

Heisss, Markus Heiss, Geometry, Würzburg
Fig.02: Further Relationships to the Lune of Hippocrates

 

All understood? Then to the next figure:

Hippocrates, Geometry,
Fig.03: Another Possibility of Construction for Squaring a Lune

 

Why this transformation to angle φ = 0° was of importance,

you will see with the help of the next drawing:

Hippocrates, curved triangle, construction
Fig.04: Construction of a Lune Segment with a Previously Defined Area

 

Testing of the relationships shown above:

(Admittedly the graphic is overloaded, but it contains all important information.)

Lune of Hippocrates, quadrature
Fig.05: Testing of the Construction of a Curved Triangle

 

Cite this as: 

Heisss, Markus:  From: https://triangle-geometry.jimdofree.com/lune-of-hippocrates-2/


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Are you interested in my other geometrical discoveries?

[here]

Contact

... to the author is maybe possible via e-mail under:   §@gmx.de   where   § = heisss

Subject: "Lune-of-Hippocrates-2"