Infinity This is a number, and may be a place. Places need not be numbered, and numbers need not denote places. So we might have geometric infinity and we can have numerical infinity, and sometimes they correspond, but as often as they do, they do not.
Alignment(1) Three
bodies as closely in a line as they can be, in any order on that line. Both
Opposition and Conjunction are Alignments. "Closeness" is usually, though not
always, reckoned in respect of differences in Geocentric longitude.
Alignment(2)
The degree to which two bodies
are aligned, wrt a third considered as vertex. The square of the cosine
of the angle subtended by the two other bodies on that vertex.
Epoch An
actual, calendar, moment; a moment in Real Time; an actual Date and Time-of-Day.
Usually for human convenience given and asked for in "Civil" date
form in the Bud Worskshop, sometimes as a Julian Date. The BW always works
with Julian epochs internally - easier, mostly because it doesn't need to take
account of leap years! A Julian Year has 365.25 days.
Leap Year
"If a year, such as 2004, is exactly divisible by 4, but
not by 100, then it is a leap year, with 366 days."
Grand
Period (GP) The whole period of a bud series,
or a whole period within which astronomical events are considered.
Inter-Alignment
Period. (IAP) The time interval between
two successive alignments.
mean Inter-Alignment
Period (mIAP) The arithmetic mean of IAPs
over a given Grand Period.
Pole In
this context, one of the two real vertices of the Semi-Imaginary
Invariant Tetrahedron judged to pertain to a real bud instance.
(IPD)
Inter-Pole Distance The
distance between the top-most, highest or tip Pole, and bottom-most, lowest
or base Pole, of a Bud.
Image
Unit (iu) The
unit
of length used by the Bud Workshop for an uncalibrated bud image. The
width of the image's frame, whatever it is in pixels, is taken to be of unit
length. The BW always uses this unit internally, but converts lengths
to the units of the current calibration , if one has been done, for display,
and for the records. It is obviously neither a standard nor a constant
unit.
Mean
Radius Deviation (MRD) Properly, the arithmetic average
of the differences between predicted and measured bud radii. In practice,
the term is used loosely and is often applied without modification to diameters
as well. And sometimes 'MRD' is used to refer to just one radius or diameter
deviation, not to the actual Mean, as in, "The MRDs on this bud varied greatly.",
meaning that the individual deviations
did. It is usually clear from context what is intended.
Standard
Error The MRD rendered in terms
of Standard Deviation, the usual statistical measure.
Semi-Imaginary
Invariant Tetrahedron When
space is transformed into itself, some elements remain invariant - they do not
move. Together, they form a tetrahedron,
which is therefore invariant. If two of the four vertices of this
tetrahedron are Real, and two
Imaginary, we have a "Semi Imaginary
Invariant Tetrahedron." All other points move (transform) in path
curves, which, however, do not themselves move. Families of invariant
path curves within this particular type of tetrahedron envelope a bud, and, highly
probably ( p > 99.9% ), exactly describe its form. This invariant
tetrahedron is accordingly the "frame" of the bud
Cross-Ratio Given that some measure is taken as standard, by that measure intervals preserve cross-ratio under projection: this means that for three adjacent intervals, a, b and c, projected from a point into intervals, a', b' and c,' on another line, we have
[(a+b)/c] / [a/(b+c)] = [(a'+b')/c'] / [a'/(b'+c')].
[Proof] Other permutations of these intervals also form cross-ratios: they differ one
from another, but all are constant.
There is a peculiar problem with regard to measurement in pure Projective Geometry[1][2]:
it does not define or preserve
absolute size—of anything. The cross-ratio is the only numeric constant,
but, as indicated already, we cannot define it or use it until one of the measures
is selected as standard.