Independent 10,284 by Wire

Wire provides us with this weekend’s first challenge.

We recall that there have been comments in the past about a perceived lack of mathematical references in Indy puzzles. This one should make up for that!
There are lots of references in the clues and solutions to terms from trigonometry and geometry.
We had some difficulty with the parsing of 9d, but when the penny dropped, we wondered why.
Thanks to Wire for the enjoyment.

completed grid

Across

1 Old ruler placed next to centre of graph (6)
SATRAP
SAT (placed) gRAPh (middle or ‘centre’ letters only)

4 Blood disorder finally beat husband … he’s out of shape (8)
THROMBUS
T (last or ‘final’ letter of ‘beat’) H (husband) + RhOMBUS (shape) without the ‘h’ (husband – ‘he’). A new word for us, but obviously related to ‘thrombosis’

10 Curiosity about icosahedron’s original volume (9)
NOISINESS
NOSINESS (curiosity) round I (first or ‘original’ letter of ‘iscosahedron’)

11 Brat hasn’t time to make mistake (5)
ERROR
tERROR (brat) without the ‘t’ (time)

12 Metal within secured carriage (5)
WAGON
AG (silver – ‘metal’) in WON (secured)

13 A prize mutt without tail circles quadrangle (9)
TRAPEZIUM
An anagram of A PRIZE MUTt without the last letter or ‘tail’ – anagrind is ‘circles’

14 Plan of rogue on street to get a diamond? (9)
STRATAGEM
RAT (rogue) after or ‘on’ ST (street) + A GEM (diamond?)

16 Where caffeine’s served two functions mostly (5)
COSTA
COS (cosine – one function in trigonometry) TAn (tangent – another) without the last letter or ‘mostly’

17 Overturn suspension of writer by university director (5)
UPEND
PEN (writer) ‘suspended’ in U (university) D (director)

19 Ten Roman men naked running short distance (9)
NANOMETRE
An anagram of TEN ROMAN and E (‘men’ without the outer letters or ‘naked’) – anagrind is ‘running’

21 Heather on bishop during dance: it’s revolting! (9)
REBELLING
LING (heather) after or ‘on’ B (bishop) in REEL (dance)

24 Attach historic Queen number (5)
ANNEX
ANNE (‘historic’ queen) X (ten in roman numerals – ‘number’)

26 He dictated ingredients of pepperoni (5)
PERON
Hidden in (‘ingredients of’) pepPERONi. A reference to Juan Peron, Argentina’s former president, considered a dictator by many.

27 Sensation in winter having 20D for Charlie? (9)
NUMBSKULL
In winter, one may have the sensation of a NUMB SKULL (‘tonsure’ – 20d)

28 Study nameless person’s DNA before trial (8)
GEOMETRY
GEnOME (person’s DNA) without the ‘n’ (name) + TRY (trial)

29 High value revolutionary joins Spain (6)
ESTEEM
MEETS (joins) E (Spain) all reversed or ‘revolutionary’

Down

1 Strength of Reds perhaps having switched ends (5)
SINEW
WINES (‘reds perhaps’) with the first and last letters or ‘ends’ switched

2 Prompt maths registration set up (7)
TRIGGER
TRIG (trigonometry – branch of maths) + REG (registration) reversed or ‘set up’ (in a down clue)

3 Lonely single approaches ‘Dateline’ in excitement (9)
ALIENATED
A (single) + an anagram of DATELINE – anagrind is ‘in excitement’

5 Plant area stood on by crowd (5)
HOSTA
A (area) under or ‘stood on by’ HOST (crowd)

6 Large empty sphere over Easter regularly eaten (5)
OBESE
OrB (sphere) without the middle letter or ’empty’ + EaStEr with alternate or ‘regular’ letters omitted or ‘eaten’

7 Fruit from edges of espalier stuffed into cheeses (7)
BERRIES
E R (first and last letters or ‘edges’ or ‘espalier’) ‘stuffed’ into BRIES (cheeses)

8 Extremely specific search for bunch of players (9)
SCRUMMAGE
S C (first and last letters or ‘extremes’ of ‘specific’) RUMMAGE (search)

9 Suffering briefly after held in US facility (8)
PENTAGON
AGONy (suffering) without the last letter or ‘briefly’ after PENT (held in)

14 Boring Maggie is half of an awkward couple (6,3)
SQUARE PEG
SQUARE (boring) PEG (Maggie) – the other half is ’round hole’

15 Commitment to one day on alternative male yoga (8)
MONOGAMY
MON (Monday – ‘day’) + an anagram of M (male) YOGA – anagrind is ‘alternative’

16 Draw curves with these school idiots (9)
COMPASSES
COMP (comprehensive school) ASSES (idiots)

18 Ban European medic boarding fabulous Greek ship (7)
EMBARGO
E (European) MB (medic) ARGO (fabulous Greek ship)

20 Haircut in Peru’s notably retro (7)
TONSURE
Hidden and reversed (‘retro’) in pERU’S NOTably

22 Weapon material incorporates nucleus of uranium (5)
LANCE
LACE (material) round or ‘incorporating’ N (middle letter or ‘nucleus’ of ‘uranium’)

23 Central core of cylinder right under cone’s lower section (5)
INNER
I (middle letter or ‘core’ of ‘cylinder’) + R (right) under NE (latter half or ‘lower section’ of ‘cone’)

25 Axes rotten elm having woody tissue (5)
XYLEM
X and Y (two axes in a graph) + an anagram of ELM – anagrind is ‘rotten’

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