Laura Anderson ; Jasbir S Chahal ; Jaap Top - The last chapter of the Disquisitiones of Gauss

hrj:8925 - Hardy-Ramanujan Journal, January 9, 2022, Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021 - https://doi.org/10.46298/hrj.2022.8925
The last chapter of the Disquisitiones of Gauss

Authors: Laura Anderson ; Jasbir S Chahal ; Jaap Top

This exposition reviews what exactly Gauss asserted and what did he prove in the last chapter of {\sl Disquisitiones Arithmeticae} about dividing the circle into a given number of equal parts. In other words, what did Gauss claim and actually prove concerning the roots of unity and the construction of a regular polygon with a given number of sides. Some history of Gauss's solution is briefly recalled, and in particular many relevant classical references are provided which we believe deserve to be better known.


Volume: Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
Published on: January 9, 2022
Accepted on: January 9, 2022
Submitted on: January 6, 2022
Keywords: Disquisitiones,ruler and compasses construction,cyclotomic polynomial,regular polygon,2010 Mathematics Subject Classification. 11-03; 12-03,[MATH]Mathematics [math]


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