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The following tables describe quintright-like multiplication for a right angle divided into various numbers of parts. Squares are shaded in red, and antisquares in green. The larger tables will help the reader surmise the underlying pattern.

Omitted are any tables where the number of parts is a multiple of three, as these will contain the element 2 cos 60° which, being rational, gives multiple ways to write zero. An open question is whether anything similar can occur when the number of parts is not a multiple of three.

By way of example, some identities are listed for the seven-part case (septrights). Other numbers of parts will often generate similar identities.

5-part
Multiplication

(quintrights)
Q
2 cos (90° / 5)
2 sin (360° / 5)
1.902113
R
2 cos (180° / 5)
2 sin (270° / 5)
1.618034
S
2 cos (270° / 5)
2 sin (180° / 5)
1.175571
T
2 cos (360° / 5)
2 sin (90° / 5)
0.618034
Q
1.902113
2 + R
3.618034
Q + S
3.077684
R + T
2.236068
S
1.175571
R
1.618034
Q + S
3.077684
2 + T
2.618034
Q
1.902113
RT
1.000000
S
1.175571
R + T
2.236068
Q
1.902113
2 − T
1.381966
QS
0.726543
T
0.618034
S
1.175571
RT
1.000000
QS
0.726543
2 − R
0.381966
  RT = RT = 1
QS = √5

7-part
Multiplication

(septrights)
Q
2 cos (90° / 7)
2 sin (540° / 7)
1.949856
R
2 cos (180° / 7)
2 sin (450° / 7)
1.801938
S
2 cos (270° / 7)
2 sin (360° / 7)
1.563663
T
2 cos (360° / 7)
2 sin (270° / 7)
1.246980
U
2 cos (450° / 7)
2 sin (180° / 7)
0.867767
V
2 cos (540° / 7)
2 sin (90° / 7)
0.445042
Some septright identities
1 ÷ R= RT
1 ÷ T= TV
1 ÷ V= V + R
 
7 ÷ Q= 3Q − 2S + U
7 ÷ S= − Q + 3S + 2U
7 ÷ U= 2Q + S + 3U
R −6+ (− T) −6+ V −6=129
R −5+ (− T) −5+ V −5= 57
R −4+ (− T) −4+ V −4= 26
R −3+ (− T) −3+ V −3= 11
R −2+ (− T) −2+ V −2= 6
R −1+ (− T) −1+ V −1= 2
R 0 + (− T) 0 + V 0 = 3
R 1 + (− T) 1 + V 1 = 1
R 2 + (− T) 2 + V 2 = 5
R 3 + (− T) 3 + V 3 = 4
R 4 + (− T) 4 + V 4 = 13
R 5 + (− T) 5 + V 5 = 16
R 6 + (− T) 6 + V 6 = 38
Q 2 + S 2 + U 2 = 7
Q 4 + S 4 + U 4 = 21
Q 6 + S 6 + U 6 = 70
Q 8 + S 8 + U 8 =245
Q
1.949856
2 + R
3.801938
Q + S
3.513519
R + T
3.048917
S + U
2.431430
T + V
1.692021
U
0.867767
R
1.801938
Q + S
3.513519
2 + T
3.246980
Q + U
2.817623
R + V
2.246980
S
1.563663
TV
0.801938
S
1.563663
R + T
3.048917
Q + U
2.817623
2 + V
2.445042
Q
1.949856
RV
1.356896
SU
0.695895
T
1.246980
S + U
2.431430
R + V
2.246980
Q
1.949856
2 − V
1.554958
QU
1.082088
RT
0.554958
U
0.867767
T + V
1.692021
S
1.563663
RV
1.356896
QU
1.082088
2 − T
0.753020
QS
0.386193
V
0.445042
U
0.867767
TV
0.801938
SU
0.695895
RT
0.554958
QS
0.386193
2 − R
0.198062
  RT + V = RTV = 1
QSU = √7

11-part
Multiplication
Q
2 cos (90° / 11)
2 sin (900° / 11)
1.979643
R
2 cos (180° / 11)
2 sin (810° / 11)
1.918986
S
2 cos (270° / 11)
2 sin (720° / 11)
1.819264
T
2 cos (360° / 11)
2 sin (630° / 11)
1.682507
U
2 cos (450° / 11)
2 sin (540° / 11)
1.511499
V
2 cos (540° / 11)
2 sin (450° / 11)
1.309721
W
2 cos (630° / 11)
2 sin (360° / 11)
1.081282
X
2 cos (720° / 11)
2 sin (270° / 11)
0.830830
Y
2 cos (810° / 11)
2 sin (180° / 11)
0.563465
Z
2 cos (900° / 11)
2 sin (90° / 11)
0.284630
Q
1.979643
2 + R
3.918986
Q + S
3.798907
R + T
3.601493
S + U
3.330763
T + V
2.992229
U + W
2.592781
V + X
2.140551
W + Y
1.644747
X + Z
1.115460
Y
0.563465
R
1.918986
Q + S
3.798907
2 + T
3.682507
Q + U
3.491142
R + V
3.228707
S + W
2.900546
T + X
2.513337
U + Y
2.074964
V + Z
1.594351
W
1.081282
XZ
0.546200
S
1.819264
R + T
3.601493
Q + U
3.491142
2 + V
3.309721
Q + W
3.060925
R + X
2.749816
S + Y
2.382729
T + Z
1.967137
U
1.511499
VZ
1.025092
WY
0.517817
T
1.682507
S + U
3.330763
R + V
3.228707
Q + W
3.060925
2 + X
2.830830
Q + Y
2.543108
R + Z
2.203616
S
1.819264
TZ
1.397877
UY
0.948034
VX
0.478891
U
1.511499
T + V
2.992229
S + W
2.900546
R + X
2.749816
Q + Y
2.543108
2 + Z
2.284630
Q
1.979643
RZ
1.634356
SY
1.255799
TX
0.851677
UW
0.430218
V
1.309721
U + W
2.592781
T + X
2.513337
S + Y
2.382729
R + Z
2.203616
Q
1.979643
2 − Z
1.715370
QY
1.416178
RX
1.088156
SW
0.737982
TV
0.372786
W
1.081282
V + X
2.140551
U + Y
2.074964
T + Z
1.967137
S
1.819264
RZ
1.634356
QY
1.416178
2 − X
1.169170
QW
0.898361
RV
0.609264
SU
0.307765
X
0.830830
W + Y
1.644747
V + Z
1.594351
U
1.511499
TZ
1.397877
SY
1.255799
RX
1.088156
QW
0.898361
2 − V
0.690279
QU
0.468144
RT
0.236479
Y
0.563465
X + Z
1.115460
W
1.081282
VZ
1.025092
UY
0.948034
TX
0.851677
SW
0.737982
RV
0.609264
QU
0.468144
2 − T
0.317493
QS
0.160379
Z
0.284630
Y
0.563465
XZ
0.546200
WY
0.517817
VX
0.478891
UW
0.430218
TV
0.372786
SU
0.307765
RT
0.236479
QS
0.160379
2 − R
0.081014
  RT + VX + Z = RTVXZ = 1
QSUWY = √11

13-part
Multiplication
Q
2 cos (90° / 13)
2 sin (1080° / 13)
1.985418
R
2 cos (180° / 13)
2 sin (990° / 13)
1.941884
S
2 cos (270° / 13)
2 sin (900° / 13)
1.870032
T
2 cos (360° / 13)
2 sin (810° / 13)
1.770912
U
2 cos (450° / 13)
2 sin (720° / 13)
1.645968
V
2 cos (540° / 13)
2 sin (630° / 13)
1.497021
W
2 cos (630° / 13)
2 sin (540° / 13)
1.326245
X
2 cos (720° / 13)
2 sin (450° / 13)
1.136129
Y
2 cos (810° / 13)
2 sin (360° / 13)
0.929446
Z
2 cos (900° / 13)
2 sin (270° / 13)
0.709210
A
2 cos (990° / 13)
2 sin (180° / 13)
0.478631
B
2 cos (1080° / 13)
2 sin (90° / 13)
0.241073
Q
1.985418
2 + R
3.941884
Q + S
3.855450
R + T
3.712796
S + U
3.516000
T + V
3.267934
U + W
2.972213
V + X
2.633151
W + Y
2.255692
X + Z
1.845339
Y + A
1.408078
Z + B
0.950283
A
0.478631
R
1.941884
Q + S
3.855450
2 + T
3.770912
Q + U
3.631385
R + V
3.438905
S + W
3.196278
T + X
2.907042
U + Y
2.575414
V + Z
2.206231
W + A
1.804877
X + B
1.377203
Y
0.929446
ZB
0.468136
S
1.870032
R + T
3.712796
Q + U
3.631385
2 + V
3.497021
Q + W
3.311663
R + X
3.078013
S + Y
2.799479
T + Z
2.480122
U + A
2.124599
V + B
1.738095
W
1.326245
XB
0.895056
YA
0.450815
T
1.770912
S + U
3.516000
R + V
3.438905
Q + W
3.311663
2 + X
3.136129
Q + Y
2.914864
R + Z
2.651093
S + A
2.348664
T + B
2.011985
U
1.645968
VB
1.255948
WA
0.847614
XZ
0.426920
U
1.645968
T + V
3.267934
S + W
3.196278
R + X
3.078013
Q + Y
2.914864
2 + Z
2.709210
Q + A
2.464049
R + B
2.182957
S
1.870032
TB
1.529839
UA
1.167336
VZ
0.787812
WY
0.396799
V
1.497021
U + W
2.972213
T + X
2.907042
S + Y
2.799479
R + Z
2.651093
Q + A
2.464049
2 + B
2.241073
Q
1.985418
RB
1.700810
SA
1.391401
TZ
1.061702
UY
0.716521
VX
0.360892
W
1.326245
V + X
2.633151
U + Y
2.575414
T + Z
2.480122
S + A
2.348664
R + B
2.182957
Q
1.985418
2 − B
1.758927
QA
1.506786
RZ
1.232674
SY
0.940586
TX
0.634783
UW
0.319722
X
1.136129
W + Y
2.255692
V + Z
2.206231
U + A
2.124599
T + B
2.011985
S
1.870032
RB
1.700810
QA
1.506786
2 − Z
1.290790
QY
1.055971
RX
0.805754
SW
0.543787
TV
0.273891
Y
0.929446
X + Z
1.845339
W + A
1.804877
V + B
1.738095
U
1.645968
TB
1.529839
SA
1.391401
RZ
1.232674
QY
1.055971
2 − X
0.863871
QW
0.659172
RV
0.444862
SU
0.224065
Z
0.709210
Y + A
1.408078
X + B
1.377203
W
1.326245
VB
1.255948
UA
1.167336
TZ
1.061702
SY
0.940586
RX
0.805754
QW
0.659172
2 − V
0.502979
QU
0.339450
RT
0.170972
A
0.478631
Z + B
0.950283
Y
0.929446
XB
0.895056
WA
0.847614
VZ
0.787812
UY
0.716521
TX
0.634783
SW
0.543787
RV
0.444862
QU
0.339450
2 − T
0.229088
QS
0.115385
B
0.241073
A
0.478631
ZB
0.468136
YA
0.450815
XZ
0.426920
WY
0.396799
VX
0.360892
UW
0.319722
TV
0.273891
SU
0.224065
RT
0.170972
QS
0.115385
2 − R
0.058116
  RT + VX + ZB = RTVXZB = 1
QSUWYA = √13


Multiplication can be extended to systems having a number of parts that is twice an odd number.

Equivalences of some constants

In the
10- and 14-part
tables
In the
5- and 7-part
tables
RQ
TR
VS
XT
ZU
BV

10-part
Multiplication
Q
2 cos (90° / 10)
2 sin (810° / 10)
1.975377
R
2 cos (180° / 10)
2 sin (720° / 10)
1.902113
S
2 cos (270° / 10)
2 sin (630° / 10)
1.782013
T
2 cos (360° / 10)
2 sin (540° / 10)
1.618034
U
2 cos (450° / 10)
2 sin (450° / 10)
1.414214
V
2 cos (540° / 10)
2 sin (360° / 10)
1.175571
W
2 cos (630° / 10)
2 sin (270° / 10)
0.907981
X
2 cos (720° / 10)
2 sin (180° / 10)
0.618034
Y
2 cos (810° / 10)
2 sin (90° / 10)
0.312869
Q
1.975377
2 + R
3.902113
Q + S
3.757390
R + T
3.520147
S + U
3.196227
T + V
2.793604
U + W
2.322195
V + X
1.793604
W + Y
1.220850
X
0.618034
R
1.902113
Q + S
3.757390
2 + T
3.618034
Q + U
3.389590
R + V
3.077684
S + W
2.689994
T + X
2.236068
U + Y
1.727082
V
1.175571
WY
0.595112
S
1.782013
R + T
3.520147
Q + U
3.389590
2 + V
3.175571
Q + W
2.883358
R + X
2.520147
S + Y
2.094882
T
1.618034
UY
1.101345
VX
0.557537
T
1.618034
S + U
3.196227
R + V
3.077684
Q + W
2.883358
2 + X
2.618034
Q + Y
2.288246
R
1.902113
SY
1.469144
TX
1.000000
UW
0.506233
U
1.414214
T + V
2.793604
S + W
2.689994
R + X
2.520147
Q + Y
2.288246
2
2.000000
QY
1.662508
RX
1.284079
SW
0.874032
TV
0.442463
V
1.175571
U + W
2.322195
T + X
2.236068
S + Y
2.094882
R
1.902113
QY
1.662508
2 − X
1.381966
QW
1.067396
RV
0.726543
SU
0.367799
W
0.907981
V + X
1.793604
U + Y
1.727082
T
1.618034
SY
1.469144
RX
1.284079
QW
1.067396
2 − V
0.824429
QU
0.561163
RT
0.284079
X
0.618034
W + Y
1.220850
V
1.175571
UY
1.101345
TX
1.000000
SW
0.874032
RV
0.726543
QU
0.561163
2 − T
0.381966
QS
0.193364
Y
0.312869
X
0.618034
WY
0.595112
VX
0.557537
UW
0.506233
TV
0.442463
SU
0.367799
RT
0.284079
QS
0.193364
2 − R
0.097887
  TX = TX = 1
RV = √5

14-part
Multiplication
Q
2 cos (90° / 14)
2 sin (1170° / 14)
1.987424
R
2 cos (180° / 14)
2 sin (1080° / 14)
1.949856
S
2 cos (270° / 14)
2 sin (990° / 14)
1.887767
T
2 cos (360° / 14)
2 sin (900° / 14)
1.801938
U
2 cos (450° / 14)
2 sin (810° / 14)
1.693448
V
2 cos (540° / 14)
2 sin (720° / 14)
1.563663
W
2 cos (630° / 14)
2 sin (630° / 14)
1.414214
X
2 cos (720° / 14)
2 sin (540° / 14)
1.246980
Y
2 cos (810° / 14)
2 sin (450° / 14)
1.064064
Z
2 cos (900° / 14)
2 sin (360° / 14)
0.867767
A
2 cos (990° / 14)
2 sin (270° / 14)
0.660558
B
2 cos (1080° / 14)
2 sin (180° / 14)
0.445042
C
2 cos (1170° / 14)
2 sin (90° / 14)
0.223929
Q
1.987424
2 + R
3.949856
Q + S
3.875191
R + T
3.751794
S + U
3.581215
T + V
3.365601
U + W
3.107662
V + X
2.810643
W + Y
2.478278
X + Z
2.114747
Y + A
1.724622
Z + B
1.312809
A + C
0.884487
B
0.445042
R
1.949856
Q + S
3.875191
2 + T
3.801938
Q + U
3.680873
R + V
3.513519
S + W
3.301980
T + X
3.048917
U + Y
2.757513
V + Z
2.431430
W + A
2.074772
X + B
1.692021
Y + C
1.287993
Z
0.867767
AC
0.436629
S
1.887767
R + T
3.751794
Q + U
3.680873
2 + V
3.563663
Q + W
3.401638
R + X
3.196835
S + Y
2.951831
T + Z
2.669705
U + A
2.354007
V + B
2.008705
W + C
1.638143
X
1.246980
YC
0.840135
ZB
0.422726
T
1.801938
S + U
3.581215
R + V
3.513519
Q + W
3.401638
2 + X
3.246980
Q + Y
3.051489
R + Z
2.817623
S + A
2.548325
T + B
2.246980
U + C
1.917377
V
1.563663
WC
1.190285
XB
0.801938
YA
0.403506
U
1.693448
T + V
3.365601
S + W
3.301980
R + X
3.196835
Q + Y
3.051489
2 + Z
2.867767
Q + A
2.647983
R + B
2.394898
S + C
2.111696
T
1.801938
UC
1.469519
VB
1.118621
WA
0.753655
XZ
0.379212
V
1.563663
U + W
3.107662
T + X
3.048917
S + Y
2.951831
R + Z
2.817623
Q + A
2.647983
2 + B
2.445042
Q + C
2.211353
R
1.949856
SC
1.663838
TB
1.356896
UA
1.032890
VZ
0.695895
WY
0.350149
W
1.414214
V + X
2.810643
U + Y
2.757513
T + Z
2.669705
S + A
2.548325
R + B
2.394898
Q + C
2.211353
2
2.000000
QC
1.763495
RB
1.504814
SA
1.227209
TZ
0.934170
UY
0.629384
VX
0.316683
X
1.246980
W + Y
2.478278
V + Z
2.431430
U + A
2.354007
T + B
2.246980
S + C
2.111696
R
1.949856
QC
1.763495
2 − B
1.554958
QA
1.326866
RZ
1.082088
SY
0.823703
TX
0.554958
UW
0.279235
Y
1.064064
X + Z
2.114747
W + A
2.074772
V + B
2.008705
U + C
1.917377
T
1.801938
SC
1.663838
RB
1.504814
QA
1.326866
2 − Z
1.132233
QY
0.923360
RX
0.702876
SW
0.473553
TV
0.238275
Z
0.867767
Y + A
1.724622
X + B
1.692021
W + C
1.638143
V
1.563663
UC
1.469519
TB
1.356896
SA
1.227209
RZ
1.082088
QY
0.923360
2 − X
0.753020
QW
0.573211
RV
0.386193
SU
0.194318
A
0.660558
Z + B
1.312809
Y + C
1.287993
X
1.246980
WC
1.190285
VB
1.118621
UA
1.032890
TZ
0.934170
SY
0.823703
RX
0.702876
QW
0.573211
2 − V
0.436337
QU
0.293976
RT
0.147918
B
0.445042
A + C
0.884487
Z
0.867767
YC
0.840135
XB
0.801938
WA
0.753655
VZ
0.695895
UY
0.629384
TX
0.554958
SW
0.473553
RV
0.386193
QU
0.293976
2 − T
0.198062
QS
0.099658
C
0.223929
B
0.445042
AC
0.436629
ZB
0.422726
YA
0.403506
XZ
0.379212
WY
0.350149
VX
0.316683
UW
0.279235
TV
0.238275
SU
0.194318
RT
0.147918
QS
0.099658
2 − R
0.050144
  TX + B = TXB = 1
RVZ = √7