My favourite APL symbol
⍟ ○*
by Roger K.W. Hui
One of the distinguishing characteristics of APL is its unique
character set, containing 150200 symbols. My favorite is
⍟
, the symbol for logarithm. Originally, the log
symbol was formed by ‘overstriking’ ○
(circle) and
*
(exponential or power). At present, ⍟
is Unicode[1] code point
0x235F
.
Reasons for liking ⍟
 It’s kind of cute, possessing a radial symmetry.

It denotes a function for which conventional mathematical
notation [2] does not have a good symbol:
⍟y ←→ ln y or log y x⍟y ←→ log_{x} y

It alludes to
0=1+*○0j1
, the most beautiful equation in all of mathematics [3], relating in one short phrase the fundamental quantities 0, 1, e, π, and0j1
and the basic operations plus, times, and exponentiation.  It is a visual pun – the symbol looks like the crosssection of a felled tree, i.e. a log [4].
Chronology
 196203
 In A Programming Language [5], logarithm, exponential, and power were not assigned symbols.
 196603

In Elementary Functions[6], exponential and power were denoted
*y
andx*y
, their definitions to this day. Natural logarithm was denoted*'
and basex
logarithm was denoted(x*)'
. (In the book,f'
is the inverse off
.)  19661127 15:53:58 (GMT7)
 Initial implementation of APL\360 [7].
 19671017

Natural logarithm was denoted by
⍟y
no later than the publication of The APL\360 Terminal System [8]. The dyadic casex⍟y
, basex
log ofy
, was undefined; instead, it was computed by a defined function in the public library workspace1 utility
[9].  196808

Finally, natural logarithm was denoted
⍟y
and the basex
logarithm ofy
was denotedx⍟y
, their definitions to this day, no later than the publication of APL\360 User’s Manual [10].
References

Unicode Consortium,
Unicode Standard 6.2,
2013
www.unicode.org/charts/PDF/U2300.pdf 
Abramowitz, Milton, and Irene A. Stegun,
Handbook of Mathematical Functions,
US National Bureau of Standards, 1964; Chapter 4
people.math.sfu.ca/~cbm/aands/page_67.htm, 
Hui, Roger K.W.,
Euler’s Identity,
J Wiki Essay, 20100204
www.jsoftware.com/jwiki/Essays/Euler's_Identity 
McDonnell, Eugene E.,
The Story of
○
, APL QuoteQuad,
Volume 8, Number 2, 197712 www.jsoftware.com/papers/eem/storyofo.htm 
Iverson, Kenneth E.,
A Programming Language,
Wiley, New York, 1962
www.jsoftware.com/papers/APL.htm 
Iverson, Kenneth E.,
Elementary Functions: An Algorithmic Treatment,
Science Research Associates, Inc., Chicago, 196603
www.jsoftware.com/jwiki/Doc/Elementary_Functions_An_Algorithmic_Treatment 
Hui, Roger K.W., (ed.),
APL Quotations and Anecdotes,
20100918
www.jsoftware.com/papers/APLQA.htm#APL_birthday 
Falkoff, Adin D. & Kenneth E. Iverson,
The APL\360 Terminal System,
Report RC1922, IBM, 19671016
www.jsoftware.com/papers/APL360TerminalSystem.htm 
Conroy, C.A., Editor,
APL\360 Newsletter Number 1,
IBM, 196707
bitsavers.informatik.unistuttgart.de/pdf/ibm/apl/APL_Newsletter_1_Jul67.pdf 
Falkoff, Adin D. & Kenneth E. Iverson,
APL\360 User’s Manual,
IBM,
196808; Table 3.2 bitsavers.informatik.unistuttgart.de/pdf/ibm/apl/APL_360_Users_Manual_Aug68.pdf