Justification about the existence and location of Chartres’ cathedral labyrinth based on astronomy and geometry

Figures & data

Figure 1. Graphical presentation of the two architectural elements considered in this paper.

Figure 2. Photographs taken by the Authors, showing the two architectural elements considered in this paper.

Figure 3. Diagram of the alignment between the rose window of the main facade, the labyrinth and the Taurus constellation. The representation of the constellation is publicly offered by the International Astronomical Union (www.iau.org).

Figure 4. Chronology of Chartres cathedral construction—astronomical epoch J1200–.

Table 1. Parameters which are intrinsic to Chartres cathedral

Location			Elements
Longitude	Latitude	Orientation	Labyrinth		Rose window
−01º 29ʹ 14ʹ’	48º 26ʹ 51ʹ’	43º 47ʹ 43ʹ’

Figure 5. Tabvla Vigesima Tertia.TAVRVS. from Uranometria, by Bayer. Universitätsbibliothek Heidelberg. http://digi.ub.uni-heidelberg.de/diglit/bayer1648/0076.

Figure 6. Geometric parameters considered in our study.

Table 2. Celestial coordinates of the main stars in Taurus constellation. We highlight the star Elthor, which is the fifth brightest of the entire constellation

			Proper Motion		J2000.0		J1200.0
Bayer	Star proper name	Flux	mas/yr in	mas/yr in	R. Ascension	Declination	R. Ascension	Declination
	Aldebaran	0.87	63.45	−188.94	04^h 35^m 55^s	12º 30ʹ 33ʹ’	03^h 50^m 30^s	14º 32ʹ 51ʹ’
	Al Nath	1.65	22.76	−173.58	05^h 26^m 17^s	28º 36ʹ 26ʹ’	04^h 36^m 08^s	27º 30ʹ 51ʹ’
	Hyadum I	3.65	115.46	−23.42	04^h 19^m 47^s	15º 37ʹ 39ʹ’	03^h 34^m 48^s	13º 21ʹ 26ʹ’
	Hyadum II	3.77	106.56	−29.18	04^h 22^m 56^s	17º 32ʹ 33ʹ’	03^h 37^m21^s	15º 19ʹ 17ʹ’
	Ain	3.53	106.19	−37.84	04^h 28^m 36^s	19º 10ʹ 49ʹ’	03^h 42^m 28^s	17º 03ʹ 10ʹ’
	Alhecka	2.97	1.78	−20.07	05^h 37^m 38^s	21º 08ʹ 33ʹ’	04^h 50^m 07^s	20º 15ʹ 19ʹ’
	Alcyone	2.85	19.34	−43.67	03^h 47^m 29^s	24º 06ʹ 18ʹ’	03^h 00^m 44^s	21º 18ʹ 39ʹ’
	Tetha I	3.85	104.97	−15.14	04^h 28^m 34^s	15º 57ʹ 43ʹ’	03^h 43^m 23^s	13º 50ʹ 13ʹ’
	Tetha II	3.41	108.42	−26.74	04^h 28^m 39^s	15º 52ʹ 15ʹ’	03^h 43^m 30^s	13º 44ʹ 59ʹ’
	Kappa I	4.21	105.1	−45.04	04^h 25^m 22^s	22º 17ʹ 37ʹ’	03^h 38^m 20^s	20º 06ʹ 18ʹ’
	Kappa II	5.28	111.97	−47.71	04^h 25^m 25^s	22º 11ʹ 59ʹ’	03^h 38^m 24^s	20º 00ʹ 45ʹ’
	Elthor	3.41	−8.02	−14.42	04^h 00^m 40^s	12º 29ʹ 25ʹ’	03^h 16^m 53^s	09º 55ʹ 01ʹ’
	Furibundus	3.89	4.72	−3.78	04^h 03^m 09^s	05º 59ʹ 21ʹ’	03^h 21^m 01^s	03º 27ʹ 59ʹ’
	Ushakaron	3.73	50.58ʹ’	−39.54	03^h 27^m 10^s	09º 43ʹ 57ʹ’	02^h44^m 20^s	06º 40ʹ 09ʹ’
	Omicron	3.62	−67.04	−78.04	03^h 24^m 48^s	09º 01ʹ 43ʹ’	02^h 42^m 16^s	05º 56ʹ 37ʹ’
	Rho	4.66	103.2	−26.48	04^h 33^m 50^s	14º 50ʹ 39ʹ’	03^h 48^m 55^s	12º 48ʹ 53ʹ’
	Omega	4.93	−39.41	−60.79	04^h 17^m 15^s	20º 34ʹ 42ʹ’	03^h 31^m 00^s	18º 15ʹ 54ʹ’
	111 Tau	5.01	105.57	−15.00	04^h 28^m 50^s	13º 02ʹ 51ʹ’	03^h 44^m 29^s	10º 56ʹ 02ʹ’
	Hyades 90	4.27	102.40	−15.78	04^h 38^m 09^s	12º 30ʹ 39ʹ’	03^h 53^m 52^s	10º 33ʹ 32ʹ’
	Hyades 88	4.25	43.13	−52.71	04^h 35^m 39^s	10º 09ʹ 38ʹ’	03^h 52^m 07^s	08º 01ʹ 50ʹ’
	30 Tau	5.07	26.00	−28.84	03^h 48^m 16^s	11º 08ʹ 35ʹ’	03^h 04^m 54^s	08º 22ʹ 59ʹ’
	5 Tau	4.10	18.25	−1.92	03^h 30^m 52^s	12º 56ʹ 12ʹ’	02^h 47^m 17^s	09º 44ʹ 44ʹ’

Figure 7. Paths on the floor plan of Chartres cathedral.

Table 3. Celestial coordinates of Elthor during the construction of Chartres cathedral

		J1194.0		J1200.0		J1226.0
Bayer	Star	R. Ascension	Declinación	R. Ascension	Declination	R. Ascension	Declination
	Elthor	03^h 16^m 34^s	09º 53ʹ 44ʹ’	03^h 16^m 53^s	09º 55ʹ 01ʹ’	03^h 18^m 21^s	10º 00ʹ 55ʹ’

Figure 8. Daily paths , and at J1200. In the centre is marked daily paths of the astronomical epochs J1194 and J1226.