Transcript Sundials: Renaissance Map Projections and Modern Equant dials Bill Gottesman, November 5, 2010

Sundials: Renaissance Map Projections
and Modern Equant dials
Bill Gottesman, November 5, 2010
What we will do today
A sundial is really just a map of
the sky
A sundial is really just a map of
the sky
A sundial is really just a map of
the sky
Tnoys Dial
Sundial and Photo by Tony Moss
Gnomonic
From United States Geological Survey web site
Gnomonic Projections
Stereographic
Very Useful Stereographic Property: Circles on
globe project as circles on flat map.
From: The Astrolabe, by James Morrison
Stereographic Projections
Orthographic
Orthographic Projections
DH1
From: The Astrolabe, by James Morrison
DH2
DH3
DH4
DH5
DH6
DH7 Mansfield Sunrise
DH8
DH9
DH10
DH11
William Oughtred
Mathematics was not his day job.
1574-1660, England
Introduced x as multiplication sign.
Introduced abbreviations sin and cos.
Invented Circular and Straight slide
rule.
Invented Ring dial and Double
Horizontal dial ~1620
Was Parish Minister of Albury.
From Wikipedia
William Oughtred
“I have heard his neighbor
ministers say that he was a pitiful
preacher; the reason was because
he never studied it, but bent all his
thoughts on the mathematiques”
-quoted by Florian Cajori in “William Oughtred”;
Open Court Publishing Co., London, 1916
From Wikipedia
“The Description and Use of the Double Horizontall Dyall: Whereby
not onely the hower of the day is showne; but also the meridian line
is found; and most astronomical questions, which may be done by
the globe, are resolved” -William Oughtred 1636
Henry Wynn’s Double Horizontal, ~1685
Wynne0
From: Sundials, by Mark Lennox-Boyd
Wynne1 Stereographic
Wynne2 Gnomonic
Wynne3 Altitude
Wynne4 Lunar
Wynne5 Epact table for moon’s
age
Wynne6 Perpetual Calendar
Wynne7 12 star nocturnal
Henry Wynn’s Double Horizontal, ~1685
Ring Dial
Analemmatic Dials, Orthographic
Projection
Invented 1640 by
Vaulezard, a little
known French
Mathematician
Circles for Peace dial
American M4 Sherman Tank, Tunisia, 1943.
Eliot Elisofon, Life Magazine
US Army Sun Compass
Sun Compass
Johann
Lambert
1728-1777 Lived mostly in
Switzerland and Germany
1772 Published on Map
Projections. Developed
concepts of Conformality
and of Equal Areas, and that
they are mutually exclusive.
1778 First to prove pi is
irrational
Johann Lambert writes
The construction of an azimuthal dial has the inconvenience that
its hour marks have to be inscribed into an ellipse, which makes
the work somewhat unwieldy. Hence I considered the problem
whether the ellipse could be replaced by a circle with an
equidistant scale. I saw immediately that the solution of the
problem would depend on the style’s direction and that it just as
little could stand still as was the case with the usual azimuthal
dials. (1775)
Foster-Lambert Sundial
Northern Switzerland
Analem1
Taken from
January 12 to
December
21, 2002, by
Anthony
Ayiomamitis
Analem2
When I was
growing up,
globes commonly
had analemmas in
the pacific ocean.
Nobody knew
what they were
for then, either.
Analem3
Equation of Time
Properly measured and published by John Flamsteed 1672; a
consequence of Huygens’ invention of the Pendulum Clock in
1656.
UVM Dial
UVM close up
UVM close up 2:15
UVM Seal
Foster-Lambert Sundial
Northern Switzerland
1923: Hugo Michnik used a Steiner Skew Projection to
invent Bifilar equi-angular (equant) dial.
(Jakob) Steiner 1796-1883 (Swiss)
Skew Projection ~1881
Stretching a gnomonic projection by a Steiner Skew
Projection gives an equant (equally spaced) dial
1923: Hugo Michnik used a Steiner Skew Projection to
invent Bifilar equi-angular (equant) dial
Fixed Gnomon Foster Lambert Dial
(Michel Vercasson, Compendium March 2010)
FL1
FL2
FL1 again
FL3
FL1 again
Pin
FL6
Hour Movement
Motto 1
Motto 2
Paint calendar on undersurface of glass and place
thin adhesive Teflon spacers under hidden areas
Sawyer 1
Equant Animation
Sawyer
Equant
Sawyer Equant
Dial
8:40
8:28
Ozanam
map
dial
(1673)
•Wind powered sundial
•Wheatstone polarizing dial
oz1
with dipleidoscope
•Civil time ring (bracelet) dial
•Ozanam map dial
•Hologram dial
oz2
12
oz3
12
oz4
12
oz5
12
oz6
12
oz7
12
oz8
12
oz9
12
oz10
12
oz11
12
oz12
12
oz14
Ozanam Map Glass overlay
Main Points to Remember:
-Sundials are Maps of the Sky
-Map Projections that generate circles and straight lines were favorites
of instruments makers in the 1600’s. This is why the Stereographic
and Gnomonic projections were so useful.
-Equant properties of some map projections (Foster-Lambert
orthographic projection and the Steiner skew projection) can be used
today to design modern dials that correct for the equation of time and
Daylight Saving. Nomographic techniques can also generate Equant
Dials (Sawyer, Ozanam).
On display in front of classroom:
-Sawyer Equant Sundial
-Original Military Abrams Sun Compass
-Reproduction Oughtred Ring dial
Bill Gottesman
www.precisionsundials.com
Questions?
Main Points to Remember:
-Sundials are Maps of the Sky
-Map Projections that generate circles and straight lines were favorites
of instruments makers in the 1600’s. This is why the Stereographic
and Gnomonic projections were so useful.
-Equant properties of some map projections (Foster-Lambert
orthographic projection and the Steiner skew projection) can be used
today to design modern dials that correct for the equation of time and
Daylight Saving. Nomographic techniques can also generate Equant
Dials (Sawyer, Ozanam).
On display in front of classroom:
-Sawyer Equant Sundial
-Original Military Abrams Sun Compass
-Reproduction Oughtred Ring dial
Bill Gottesman
www.precisionsundials.com