On Stonehenge and its Moving Shadows

O Sto ehe ge a d its Mo i g Shado s

Di it ios S. De d i os

E e itus P ofesso , “ hool of A hite tu e a d U a Desig , U i e sit of

Ka sas, La e e, Ka sas, U“A.

I Reside e at O o d Bea h, Flo ida, U“A.

Co ta t:

f-jf@ea thli k. et

Ma h ,

Ta le of Co te ts

A st a t

I t odu tio

Basi P i iples i Shado D a i s

O the A hite tu e of Sto ehe ge

The sa se s’ oute i g itals The T ilitho s e se le

The athe ati al odulus at Sto ehe ge The T ilitho s uasi-ellipti al a

Alig e ts at Sto ehe ge e o d the su e solsti e su ise

The shado s of Sto ehe ge a d thei o e e t i spa e-ti e

The sho t sha p shado s a d Sto ehe ge II ke shado le gth The lo g shado s a d the li ks of the o u e t to its e i o s

So e ge e al thoughts o the e lo g shado s A li tel’s shado

Co lusio s a d suggestio s fo fu the esea h

Notes

Note

.

Ne o ’s o k

Note

. Wh lu a ased o u e ts?

Note

. The B itish He itage sou es

Note

. Mo e o the odulus at Kasta Tu ulus

A st a t

The pape is set to a al ze the shado s of “to ehe ge Phase II i a - BC . “u h a stud , the pape sho s, allo s o e to de i e plausi le h potheses ega di g the desig spe ifi atio s of the o u e t, i ludi g the height of the t o sets of sa se s i oth sto e e losu es, the dia ete of the oute i le, as ell as the i e T ilitho s e se le fo a d di e sio s. Afte so e ge e al p i iples ega di g the d a i s of shado s a e p ese ted, the pape e a i es i detail the A hite tu e of the o u e t’s t o sto e e losu es. The pape does ot add ess the t o Bluesto e e losu es. It ide tifies the fo of the T ilitho s e se le as a si ple lass, of the sto e e losu es lassifi atio s he e p oposed Ale a de Tho . This suggested si ple lass of e losu es as dete ted the autho to also des i e the A hite tu e of Go ekli Tepe’s st u tu e D La e III.

A athe ati al odulus is ide tified fo the o u e t. It depi ts ke atios a o g the asi o stitue t ele e ts of “to ehe ge II floo pla . The pape pi poi ts the o phalos of the o u e t as ei g the e te of the oute sa se s i le, a d the a e te of the e ti e Phase II st u tu e. Fu the , the pape a al zes the “to ehe ge II shado s a d fi ds that the spatial le gth ise easu e of the o u e t’s odulus is li ked to the le gth of the shado ast-off the oute i g’s sa se s i ludi g thei li tels at oo ti e at e ui o , spe ifi all a le gth of a out si ete s.

The pape , utilizes the o k Ne o alo g ith p e ious o k the autho , as to the i po ta e of a phase t a sitio i the d a i s go e i g the th ee fu tio s des i i g the ast-off sha p “u -i du ed shado s’ le gths o e a ea . This phase t a sitio takes pla e du i g the e al a d autu al e ui o . Whe e, the pape ide tifies the e ui o oo ti e alig e t to ha e ee sig ifi a t also i the desig of “to ehe ge II, esides the do i a t a d ell dis ussed i the lite atu e su ise at su e solsti e alig e t. The sig ifi a e of the i te solsti e su set alig e t is also dis ussed i efe e e to the T ilitho s e se le.

Nu e ous e te sio s of the o k a e suggested, as the a al sis of “to ehe ge II shado s ope s up a e i do i to a al zi g the o u e t, its desig , a d possi l its ultu e elated

Figu e . The sha p le gths of shado s. Dail a d a ual paths of total “u -i du ed ast off shado le gths a e sho i this a o d a i s odel p oposed the autho i efe e e [ . ] A {EA D} is the st le’s t aje to ide tified fu tio  du i g the da of the su e solsti e; a {GA F} is the st le’s t aje to du i g e ui o es, fu tio  ; a d a {CA B} is the st le’s t aje to du i g i te solsti e, fu tio  , at so e lo atio he e the solsti es appea at a a gle ω. As dis ussed i [ . ], a ious su - egio s ithi egio R see pape ’s a ati e fo its defi itio ide tif g ou d ased ale da a d lo k fu tio s fo the e hi a ti g as a g o o of a su dial ith a st le o its e top poi t. I side the shaded a ea, the e hi loses its g ou d ased ale da i di ati g p ope t , etai i g o l its lo k i di ati g apa ilit . Of ou se, if a othe e hi is aised i side the shaded a ea the the al ulus is diffe e t. Co se ue tl , fo a o u e t ith ultiple e hi s, the shaded a ea a ui es spe ial i te est. As e tio ed i the te t, these fu tio s hide i the alig e t fu tio s, due to the

its latitude . Thus, i all ases of o u e ts he e ultiple e hi s o thostats, pilla s, olu s, o elisks et . a e i ol ed, this shaded a ea of Figu e a ui es pa ti ula i po ta e. At a lo atio , o th of fu tio  a d south of fu tio  , g ou d ased ale da i di atio s a o l e o tai ed et ee the su e solsti e a d the autu al e ui o , a d the ti e pe iod et ee the sp i g e ui o a d the su e solsti e. A d at a lo atio , o th of fu tio  a d south of fu tio  g ou d ased ale da i di atio s a e o tai ed i the seaso s et ee the autu al e ui o a d the i te solsti e, as ell as du i g the i te solsti e a d the sp i g e ui o . A d agai , the al ulus ha ges if e hi s of app op iate height a e aised ithi these su - egio s. Natu all , the ould e of de easi g apa ilit to a t as

ale da i di ato s the fu the a a the a e f o the shaded a ea of Figu e .

Figu e . This is a figu e sho i g shado s of o je ts f o diffe e t dista es. It as a al zed a d e te si el dis ussed i [ . ]. The photo de o st ates t o fu da e tal p ope ties of shado s, a el thei fuzz atu e a d the effe t dista e has o the . “ou e: the autho a d

Figu e . The N-“ a d E-W a es of “to ehe ge, at p ese t azi uths ith the e te of the pla e dete i i g the azi uths at the e e te of the oute i g i le – this ei g the o u e t’s

Figu e . The ajo alig e ts ith O as the o u e t’s o phalos. The A hite tu e a d Ast o o of “to ehe ge Phase II o tai s the sa se s i le a d the T ilitho s’ uasi-ellipti al o pholog . The T ilitho s’ sto e e losu e o figu atio o sists of t o se i i les ith pa allel dia ete s AB a d CD sepa ated a dista e of a out . ete s. It o tai s the st u tu e’s ai alig e t the su e solsti e su ise as its ajo a is. It is si ila to the sto e e losu e ide tified the autho as the luep i t of Go ekli Tepe st u tu e D, La e III, see [ . ], [ . ]. Both a e si ple e sio s of the Tho ’s sto e e losu e lassifi atio s he e fo Neolithi

O the shado s of Sto ehe ge a d thei o e e t i spa e-ti e

I hat follo s, so e use is ade of ast o o i al i fo atio a d te s, although the pape is add essed to a ge e al audie e. The athe ati all i li ed eade is di e ted to a lassi al efe e e f o o su je ts o e ed he e, see “i o Ne o [ . ]. Fo o e o the efe e e, see Note . Mu h has ee itte o “to ehe ge’s Ast o o , see fo a ief e ie the autho ’s efe e e i [ . ]. A ke od of o k i this dis ussio is Ale a de Tho ’s iti gs i [ . ], that has i spi ed a e eed of a haeo-ast o o e s ith a spe ial fo us o Neolithi

o u e ts of the B itish Isles a d B itta like fo e a ple, Au e Bu l, see [ . ] .

Figu e .a. Google Ea th ap of “to ehe ge, take o August , . The photo is f o a altitude of a out feet; “to ehe ge’s ele atio is app o i atel feet. Its ap poi te

oo di ates a e:  ’ N,  ’ W. This oo di ate i plies that at su e solsti e oo

Figu e . . E ui o da , oo ti e shado s. “to ehe ge Phase II a d its dual, the shado ast so e of its T ilitho s e se le pilla s a d the li tels of the o pleted, i theo oute i g. The ke dista e of a out si ete s is depi ted; that is he e the shado f o the oute -sa se s i g st u tu e tou hes the oute ski su fa e of the T ilitho s e se le a d the dista e

Figu e .a. The “to ehe ge II floo pla du i g su ise at su e solsti e. The sho t pa t of the e lo g su ise shado s is sho i side the sa se s oute i le. O l the ast-off shado s f o still sta di g sa se s i the oute i g a d the T ilitho s e se le a e d a . The su a s a e pa allel li es. “ou e: the autho .

t o o e to that ope i g’s eithe side: that et ee # a d # to the No th a d et ee # a d # to the “outh. These th ee slits allo fo a o plete pe et atio of the floo pla . Whe eas the e t t o that et ee # a d # , as ell as that et ee # a d # a e ot t a slu e t, as su a s fall o T ilitho s E se le sa se s. To the No th of # a d “outh of # the floo pla of the o u e t is i shade.

I Figu e . , the sa e o ditio s a e sho ut fo the su ise at e ui o . “to es # , # , # a d # of the T ilitho s e se le o attai sig ifi a t i po ta e, as the e o e the ai e epto s of the su ise a s i side the o u e t’s i e sa tu . The i po ta e of the e al e ui o has al ead ee add essed i the te t, as it as the i po ta e a d asso iated

a i gs of sto e # .

I this Note, a e a k ade i the ai te t of the pape ill e fu the ela o ated. The pape e tio ed the o u e t as so- alled at p ese t “to ehe ge at a pla e u e tl alled Wiltshi e at a pla e alled “alis u Plai . It as e tio ed i su h a a e of ou se, e ause

these a e u e t te s a d o e latu e ega di g topo s a d o u e ts that u e t

so io- ultu al o ditio s e plo i la eli g o u e ts a d sites.

Figu e N . The th ee ajo Phases of the “to ehe ge o ple , ith the a ious o po e ts of the o u e t. The da k se tio is the pa t studied i this pape . Lo atio of a ious sto es asso iated ith the Phase II o u e t o ie tatio heal a d slaughte sto es a e i di ated at the otto diag a . The sto e ot sho he e a d of i po t is the alta sto e, l i g just i f o t of the “outh este t ilitho set, at the e e te he e the slit et ee its t o up ights

Refe e es

[ . ] https://ka sas.a ade ia.edu/Di it iosDe d i os

[ . ] Di it ios “. De d i os, Θa ua , A P i e o Go ekli Tepe , a ade ia.edu. :

https:// .a ade ia.edu/ /A_P i e _o _Go ekli_Tepe

Othe sou es

[ . ] B A tho Θoh so - D a Autho AΘ , a o pute o pilatio of data f o a ious su e s., CC BY . , https:// o o s. iki edia.o g/ /i de .php? u id=

[ . ] http:// .e glish-he itage.o g.uk/ isit/pla es/sto ehe ge/histo /

[ . ] “i o Ne o , , A Co pe diu of Sphe i al Ast o o : ith its appli atio s to

the dete i atio a d edu tio of positio s of the fi ed sta s, Ma Milla , Ne Yo k. I ele t o i fo the ook is he e:

https:// ooks.google. o / ooks?id=CA DAAAAIAAΘ&p i tse =f o t o e &sou e=g s_ge_su a _ & ad= # =o epage& &f=false

[ . ] Ale a de Tho , , Megalithi Lu a O se atio s, O fo d U i e sit P ess, O fo d. [ . ] Au e Bu l, , The Sto e Ci les of the B itish Isles, Yale U i e sit P ess, Ne Hea e . [ . ] Ale a de Tho , A hi ald “. Tho , , Megalithi Re ai s i B itai a d B itta , Cla e do P ess, O fo d.

[ . ] G. Te e e Meade , , “to ehe ge a d A e u : egalithi shado asti g at the

solsti es at su ise , fo th o i g i the Journal of Lithic Studies.

[ . ] A highl spe ialized log is that the a e Do ou look at shado s fou d he e:

http:// . egalithi . o.uk/ odules.php?op= odload& a e=Fo u &file= ie topi &topi = &fo u = &sta t=

It is hosted the site Megalithi Po tal fou d he e: http:// . egalithi . o.uk/i de .php

[ . ] G. Te e e Meade , , D o e g “to e Ci le, “W I ela d: desig pla a al zed ith

espe t to su ises a d lithi shado - asti g fo the eight t aditio al ag i ultu al festi al dates – a d fu the alidated photog aph , fo th o i g i the Journal of Lithic Studies.

[ . ] https:// .fa e ook. o /g oups/ /pe ali k/ /

[ . ] Rose a Hill, , “to ehe ge, p ofile Books, Lo do . The ook is also fou d he e:

https:// ooks.google. o /

ooks?id=-W I YK K C&pg=PA &lpg=PA &d =pete +Ne ha +a d+the+“tatio +“to es# =o epa ge& =pete % Ne ha % a d% the% “tatio % “to es&f=false

A k o ledge e ts

The autho ishes to a k o ledge the o t i utio s ade to this pape th ough his i te a tio ith e e s of the Megalithi Po tal e site http:// . egalithi . o.uk/i de .php . The autho ishes to tha k the site a age A d Bu ha ; a d also, the e e s of the su -g oup i it Do ou look at the shado s . Withi this g oup, i spe ifi , the autho ishes to e og ize the o t i utio s Da id “ th E e g a , Neil Wise a Fea o , a d Ri ha d Ba tosz O p it . Da id “ th has ee i st u e tal i e ou agi g the autho to pa ti ipate i that g oup, a d fo i t odu i g the autho ’s p io o k to the g oup e e s.

Fu the o e, the autho ishes to e og ize his Fa e ook f ie ds a d espe iall those ho a e e e s of the se e g oups the autho has eated a d is ad i iste i g. Thei o ti uous i telle tual a d a tisti sti ulatio a d suppo t ha e ee e a ka le a d thus a g eat se se of g atitude is e te ded to the as ell. “pe ial e tio ust e ade to P ofesso Te e e Meade fo his o t i utio , a d espe iall his o k o the shado s at D o eg a d “to ehe ge.

But ost i po ta t a d dee to this autho s has ee the o e tha ea s of e ou age e t a d suppo t he has e ei ed f o his ife Cathe i e a d thei daughte s Daph e-I is a d Ale ia-A te is. Thei o ti ui g assista e a d u de sta di g fo all those lo g hou s he spe t o doi g

esea h, he he ould ha e allotted ti e ith the , this autho ill al a s e deepl app e iati e.

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