Mnogokotniško število: Razlika med redakcijama

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Če je ''s'' število stranic mnogokotnika, je enačba za ''n''-to ''s''-mnogokotniško število (''n''/2) ((''s''-2)''n'' - (4-''s'')).
Če je ''s'' število stranic mnogokotnika, je enačba za ''n''-to ''s''-mnogokotniško število (''n''/2) ((''s''-2)''n'' - (4-''s'')).
{| border="1" cellpadding="3" cellspacing="0" bordercolor="#000000"

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<table border="1" cellpadding="3" cellspacing="0" bordercolor="#000000"><tr><b>
<b>
<td align=center bgcolor="#A0E0A0">'''Ime'''</td><td align=center bgcolor="#A0E0A0">'''Ena&#269;ba'''</td><td align=center bgcolor="#A0E0A0">'''<i>n</i>=1'''</td><td align=center bgcolor="#A0E0A0">'''2'''</td><td align=center bgcolor="#A0E0A0">'''3'''</td><td align=center bgcolor="#A0E0A0">'''4'''</td><td align=center bgcolor="#A0E0A0">'''5'''</td><td align=center bgcolor="#A0E0A0">'''6'''</td><td align=center bgcolor="#A0E0A0">'''7'''</td><td align=center bgcolor="#A0E0A0">'''8'''</td><td align=center bgcolor="#A0E0A0">'''9'''</td><td align=center bgcolor="#A0E0A0">'''10'''</td><td align=center bgcolor="#A0E0A0">'''11'''</td><td align=center bgcolor="#A0E0A0">'''12'''</td><td align=center bgcolor="#A0E0A0">'''13'''</td></b></tr>
| align="center" bgcolor="#A0E0A0" | '''Ime'''
<tr><td align=center>[[trikotniško število|Trikotniško]]</td><td align=center>½<i>n</i>(1<i>n</i> + 1)</td>
| align="center" bgcolor="#A0E0A0" | '''Ena&#269;ba'''
<td align=right>1</td><td align=right>3</td><td align=right>6</td><td align=right>10</td><td align=right>15</td><td align=right>21</td><td align=right>28</td><td align=right>36</td><td align=right>45</td><td align=right>55</td><td align=right>66</td><td align=right>78</td><td align=right>91</td></tr>
<tr><td align=center>[[kvadratno število|Kvadratno]]</td><td align=center>½<i>n</i>(2<i>n</i> - 0)</td>
| align="center" bgcolor="#A0E0A0" | '''<i>n</i>=1'''
| align="center" bgcolor="#A0E0A0" | '''2'''
<td align=right>1</td><td align=right>4</td><td align=right>9</td><td align=right>16</td><td align=right>25</td><td align=right>36</td><td align=right>49</td><td align=right>64</td><td align=right>81</td><td align=right>100</td><td align=right>121</td><td align=right>144</td><td align=right>169</td></tr>
| align="center" bgcolor="#A0E0A0" | '''3'''
<tr><td align=center>[[peterokotniško število|Peterokotniško]]</td><td align=center>½<i>n</i>(3<i>n</i> - 1)</td>
| align="center" bgcolor="#A0E0A0" | '''4'''
<td align=right>1</td><td align=right>5</td><td align=right>12</td><td align=right>22</td><td align=right>35</td><td align=right>51</td><td align=right>70</td><td align=right>92</td><td align=right>117</td><td align=right>145</td><td align=right>176</td><td align=right>210</td><td align=right>247</td></tr>
| align="center" bgcolor="#A0E0A0" | '''5'''
<tr><td align=center>[[šesterokotniško število|Šesterokotniško]]</td><td align=center>½<i>n</i>(4<i>n</i> - 2)</td>
| align="center" bgcolor="#A0E0A0" | '''6'''
<td align=right>1</td><td align=right>6</td><td align=right>15</td><td align=right>28</td><td align=right>45</td><td align=right>66</td><td align=right>91</td><td align=right>120</td><td align=right>153</td><td align=right>190</td><td align=right>231</td><td align=right>276</td><td align=right>325</td></tr>
| align="center" bgcolor="#A0E0A0" | '''7'''
<tr><td align=center>[[sedmerokotniško število|Sedmerokotniško]]</td><td align=center>½<i>n</i>(5<i>n</i> - 3)</td>
| align="center" bgcolor="#A0E0A0" | '''8'''
<td align=right>1</td><td align=right>7</td><td align=right>18</td><td align=right>34</td><td align=right>55</td><td align=right>81</td><td align=right>112</td><td align=right>148</td><td align=right>189</td><td align=right>235</td><td align=right>286</td><td align=right>342</td><td align=right>403</td></tr>
| align="center" bgcolor="#A0E0A0" | '''9'''
<tr><td align=center>[[osmerokotniško število|Osmerokotniško]]</td><td align=center>½<i>n</i>(6<i>n</i> - 4)</td>
| align="center" bgcolor="#A0E0A0" | '''10'''
<td align=right>1</td><td align=right>8</td><td align=right>21</td><td align=right>40</td><td align=right>65</td><td align=right>96</td><td align=right>133</td><td align=right>176</td><td align=right>225</td><td align=right>280</td><td align=right>341</td><td align=right>408</td><td align=right>481</td></tr>
| align="center" bgcolor="#A0E0A0" | '''11'''
<tr><td align=center>[[deveterokotniško število|Deveterokotniško]]</td><td align=center>½<i>n</i>(7<i>n</i> - 5)</td>
| align="center" bgcolor="#A0E0A0" | '''12'''
<td align=right>1</td><td align=right>9</td><td align=right>24</td><td align=right>46</td><td align=right>75</td><td align=right>111</td><td align=right>154</td><td align=right>204</td><td align=right>261</td><td align=right>325</td><td align=right>396</td><td align=right>474</td><td align=right>559</td></tr>
| align="center" bgcolor="#A0E0A0" | '''13'''</b>
<tr><td align=center>[[deseterokotniško število|Deseterokotniško]]</td><td align=center>½<i>n</i>(8<i>n</i> - 6)</td>
|-----
<td align=right>1</td><td align=right>10</td><td align=right>27</td><td align=right>52</td><td align=right>85</td><td align=right>126</td><td align=right>175</td><td align=right>232</td><td align=right>297</td><td align=right>370</td><td align=right>451</td><td align=right>540</td><td align=right>637</td></tr>
| align="center" | [[trikotniško število|Trikotniško]]
<tr><td align=center>11-kotniško</td><td align=center>½<i>n</i>(9<i>n</i> - 7)</td>
| align="center" | ½<i>n</i>(1<i>n</i> + 1)
<td align=right>1</td><td align=right>11</td><td align=right>30</td><td align=right>58</td><td align=right>95</td><td align=right>141</td><td align=right>196</td><td align=right>260</td><td align=right>333</td><td align=right>415</td><td align=right>506</td><td align=right>606</td><td align=right>715</td></tr>
| align="right" | 1 || align="right" | 3
<tr><td align=center>12-kotniško</td><td align=center>½<i>n</i>(10<i>n</i> - 8)</td>
| align="right" | 6
<td align=right>1</td><td align=right>12</td><td align=right>33</td><td align=right>64</td><td align=right>105</td><td align=right>156</td><td align=right>217</td><td align=right>288</td><td align=right>369</td><td align=right>460</td><td align=right>561</td><td align=right>672</td><td align=right>793</td></tr>
| align="right" | 10 || align="right" | 15
<tr><td align=center>13-kotniško</td><td align=center>½<i>n</i>(11<i>n</i> - 9)</td>
| align="right" | 21
<td align=right>1</td><td align=right>13</td><td align=right>36</td><td align=right>70</td><td align=right>115</td><td align=right>171</td><td align=right>238</td><td align=right>316</td><td align=right>405</td><td align=right>505</td><td align=right>616</td><td align=right>738</td><td align=right>871</td></tr>
| align="right" | 28 || align="right" | 36
<tr><td align=center>14-kotniško</td><td align=center>½<i>n</i>(12<i>n</i> - 10)</td>
| align="right" | 45
<td align=right>1</td><td align=right>14</td><td align=right>39</td><td align=right>76</td><td align=right>125</td><td align=right>186</td><td align=right>259</td><td align=right>344</td><td align=right>441</td><td align=right>550</td><td align=right>671</td><td align=right>804</td><td align=right>949</td></tr>
| align="right" | 55 || align="right" | 66
<tr><td align=center>15-kotniško</td><td align=center>½<i>n</i>(13<i>n</i> - 11)</td>
| align="right" | 78 || align="right" | 91
<td align=right>1</td><td align=right>15</td><td align=right>42</td><td align=right>82</td><td align=right>135</td><td align=right>201</td><td align=right>280</td><td align=right>372</td><td align=right>477</td><td align=right>595</td><td align=right>726</td><td align=right>870</td><td align=right>1027</td></tr>
|-----
<tr><td align=center>16-kotniško</td><td align=center>½<i>n</i>(14<i>n</i> - 12)</td>
| align="center" | [[kvadratno število|Kvadratno]]
<td align=right>1</td><td align=right>16</td><td align=right>45</td><td align=right>88</td><td align=right>145</td><td align=right>216</td><td align=right>301</td><td align=right>400</td><td align=right>513</td><td align=right>640</td><td align=right>781</td><td align=right>936</td><td align=right>1105</td></tr>
<tr><td align=center>17-kotniško</td><td align=center>½<i>n</i>(15<i>n</i> - 13)</td>
| align="center" | ½<i>n</i>(2<i>n</i> - 0)
| align="right" | 1 || align="right" | 4
<td align=right>1</td><td align=right>17</td><td align=right>48</td><td align=right>94</td><td align=right>155</td><td align=right>231</td><td align=right>322</td><td align=right>428</td><td align=right>549</td><td align=right>685</td><td align=right>836</td><td align=right>1002</td><td align=right>1183</td></tr>
| align="right" | 9
<tr><td align=center>18-kotniško</td><td align=center>½<i>n</i>(16<i>n</i> - 14)</td>
| align="right" | 16 || align="right" | 25
<td align=right>1</td><td align=right>18</td><td align=right>51</td><td align=right>100</td><td align=right>165</td><td align=right>246</td><td align=right>343</td><td align=right>456</td><td align=right>585</td><td align=right>730</td><td align=right>891</td><td align=right>1068</td><td align=right>1261</td></tr>
| align="right" | 36
<tr><td align=center>19-kotniško</td><td align=center>½<i>n</i>(17<i>n</i> - 15)</td>
| align="right" | 49 || align="right" | 64
<td align=right>1</td><td align=right>19</td><td align=right>54</td><td align=right>106</td><td align=right>175</td><td align=right>261</td><td align=right>364</td><td align=right>484</td><td align=right>621</td><td align=right>775</td><td align=right>946</td><td align=right>1134</td><td align=right>1339</td></tr>
| align="right" | 81
<tr><td align=center>20-kotniško</td><td align=center>½<i>n</i>(18<i>n</i> - 16)</td>
| align="right" | 100 || align="right" | 121
<td align=right>1</td><td align=right>20</td><td align=right>57</td><td align=right>112</td><td align=right>185</td><td align=right>276</td><td align=right>385</td><td align=right>512</td><td align=right>657</td><td align=right>820</td><td align=right>1001</td><td align=right>1200</td><td align=right>1417</td></tr>
| align="right" | 144 || align="right" | 169
<tr><td align=center>21-kotniško</td><td align=center>½<i>n</i>(19<i>n</i> - 17)</td>
|-----
<td align=right>1</td><td align=right>21</td><td align=right>60</td><td align=right>118</td><td align=right>195</td><td align=right>291</td><td align=right>406</td><td align=right>540</td><td align=right>693</td><td align=right>865</td><td align=right>1056</td><td align=right>1266</td><td align=right>1495</td></tr>
| align="center" | [[peterokotniško število|Peterokotniško]]
<tr><td align=center>22-kotniško</td><td align=center>½<i>n</i>(20<i>n</i> - 18)</td>
| align="center" | ½<i>n</i>(3<i>n</i> - 1)
<td align=right>1</td><td align=right>22</td><td align=right>63</td><td align=right>124</td><td align=right>205</td><td align=right>306</td><td align=right>427</td><td align=right>568</td><td align=right>729</td><td align=right>910</td><td align=right>1111</td><td align=right>1332</td><td align=right>1573</td></tr>
| align="right" | 1 || align="right" | 5
<tr><td align=center>23-kotniško</td><td align=center>½<i>n</i>(21<i>n</i> - 19)</td>
| align="right" | 12
<td align=right>1</td><td align=right>23</td><td align=right>66</td><td align=right>130</td><td align=right>215</td><td align=right>321</td><td align=right>448</td><td align=right>596</td><td align=right>765</td><td align=right>955</td><td align=right>1166</td><td align=right>1398</td><td align=right>1651</td></tr>
| align="right" | 22 || align="right" | 35
<tr><td align=center>24-kotniško</td><td align=center>½<i>n</i>(22<i>n</i> - 20)</td>
| align="right" | 51
<td align=right>1</td><td align=right>24</td><td align=right>69</td><td align=right>136</td><td align=right>225</td><td align=right>336</td><td align=right>469</td><td align=right>624</td><td align=right>801</td><td align=right>1000</td><td align=right>1221</td><td align=right>1464</td><td align=right>1729</td></tr>
| align="right" | 70 || align="right" | 92
<tr><td align=center>25-kotniško</td><td align=center>½<i>n</i>(23<i>n</i> - 21)</td>
| align="right" | 117
<td align=right>1</td><td align=right>25</td><td align=right>72</td><td align=right>142</td><td align=right>235</td><td align=right>351</td><td align=right>490</td><td align=right>652</td><td align=right>837</td><td align=right>1045</td><td align=right>1276</td><td align=right>1530</td><td align=right>1807</td></tr>
| align="right" | 145 || align="right" | 176
<tr><td align=center>26-kotniško</td><td align=center>½<i>n</i>(24<i>n</i> - 22)</td>
| align="right" | 210 || align="right" | 247
<td align=right>1</td><td align=right>26</td><td align=right>75</td><td align=right>148</td><td align=right>245</td><td align=right>366</td><td align=right>511</td><td align=right>680</td><td align=right>873</td><td align=right>1090</td><td align=right>1331</td><td align=right>1596</td><td align=right>1885</td></tr>
|-----
<tr><td align=center>27-kotniško</td><td align=center>½<i>n</i>(25<i>n</i> - 23)</td>
| align="center" | [[šesterokotniško število|Šesterokotniško]]
<td align=right>1</td><td align=right>27</td><td align=right>78</td><td align=right>154</td><td align=right>255</td><td align=right>381</td><td align=right>532</td><td align=right>708</td><td align=right>909</td><td align=right>1135</td><td align=right>1386</td><td align=right>1662</td><td align=right>1963</td></tr>
<tr><td align=center>28-kotniško</td><td align=center>½<i>n</i>(26<i>n</i> - 24)</td>
| align="center" | ½<i>n</i>(4<i>n</i> - 2)
| align="right" | 1 || align="right" | 6
<td align=right>1</td><td align=right>28</td><td align=right>81</td><td align=right>160</td><td align=right>265</td><td align=right>396</td><td align=right>553</td><td align=right>736</td><td align=right>945</td><td align=right>1180</td><td align=right>1441</td><td align=right>1728</td><td align=right>2041</td></tr>
| align="right" | 15
<tr><td align=center>29-kotniško</td><td align=center>½<i>n</i>(27<i>n</i> - 25)</td>
| align="right" | 28 || align="right" | 45
<td align=right>1</td><td align=right>29</td><td align=right>84</td><td align=right>166</td><td align=right>275</td><td align=right>411</td><td align=right>574</td><td align=right>764</td><td align=right>981</td><td align=right>1225</td><td align=right>1496</td><td align=right>1794</td><td align=right>2119</td></tr>
| align="right" | 66
<tr><td align=center>30-kotniško</td><td align=center>½<i>n</i>(28<i>n</i> - 26)</td>
| align="right" | 91 || align="right" | 120
<td align=right>1</td><td align=right>30</td><td align=right>87</td><td align=right>172</td><td align=right>285</td><td align=right>426</td><td align=right>595</td><td align=right>792</td><td align=right>1017</td><td align=right>1270</td><td align=right>1551</td><td align=right>1860</td><td align=right>2197</td></tr>
| align="right" | 153
</table>
| align="right" | 190 || align="right" | 231
| align="right" | 276 || align="right" | 325
|-----
| align="center" | [[sedmerokotniško število|Sedmerokotniško]]
| align="center" | ½<i>n</i>(5<i>n</i> - 3)
| align="right" | 1 || align="right" | 7
| align="right" | 18
| align="right" | 34 || align="right" | 55
| align="right" | 81
| align="right" | 112 || align="right" | 148
| align="right" | 189
| align="right" | 235 || align="right" | 286
| align="right" | 342 || align="right" | 403
|-----
| align="center" | [[osmerokotniško število|Osmerokotniško]]
| align="center" | ½<i>n</i>(6<i>n</i> - 4)
| align="right" | 1 || align="right" | 8
| align="right" | 21
| align="right" | 40 || align="right" | 65
| align="right" | 96
| align="right" | 133 || align="right" | 176
| align="right" | 225
| align="right" | 280 || align="right" | 341
| align="right" | 408 || align="right" | 481
|-----
| align="center" | [[deveterokotniško število|Deveterokotniško]]
| align="center" | ½<i>n</i>(7<i>n</i> - 5)
| align="right" | 1 || align="right" | 9
| align="right" | 24
| align="right" | 46 || align="right" | 75
| align="right" | 111
| align="right" | 154 || align="right" | 204
| align="right" | 261
| align="right" | 325 || align="right" | 396
| align="right" | 474 || align="right" | 559
|-----
| align="center" | [[deseterokotniško število|Deseterokotniško]]
| align="center" | ½<i>n</i>(8<i>n</i> - 6)
| align="right" | 1 || align="right" | 10
| align="right" | 27
| align="right" | 52 || align="right" | 85
| align="right" | 126
| align="right" | 175 || align="right" | 232
| align="right" | 297
| align="right" | 370 || align="right" | 451
| align="right" | 540 || align="right" | 637
|-----
| align="center" | 11-kotniško
| align="center" | ½<i>n</i>(9<i>n</i> - 7)
| align="right" | 1 || align="right" | 11
| align="right" | 30
| align="right" | 58 || align="right" | 95
| align="right" | 141
| align="right" | 196 || align="right" | 260
| align="right" | 333
| align="right" | 415 || align="right" | 506
| align="right" | 606 || align="right" | 715
|-----
| align="center" | 12-kotniško
| align="center" | ½<i>n</i>(10<i>n</i> - 8)
| align="right" | 1 || align="right" | 12
| align="right" | 33
| align="right" | 64 || align="right" | 105
| align="right" | 156
| align="right" | 217 || align="right" | 288
| align="right" | 369
| align="right" | 460 || align="right" | 561
| align="right" | 672 || align="right" | 793
|-----
| align="center" | 13-kotniško
| align="center" | ½<i>n</i>(11<i>n</i> - 9)
| align="right" | 1 || align="right" | 13
| align="right" | 36
| align="right" | 70 || align="right" | 115
| align="right" | 171
| align="right" | 238 || align="right" | 316
| align="right" | 405
| align="right" | 505 || align="right" | 616
| align="right" | 738 || align="right" | 871
|-----
| align="center" | 14-kotniško
| align="center" | ½<i>n</i>(12<i>n</i> - 10)
| align="right" | 1 || align="right" | 14
| align="right" | 39
| align="right" | 76 || align="right" | 125
| align="right" | 186
| align="right" | 259 || align="right" | 344
| align="right" | 441
| align="right" | 550 || align="right" | 671
| align="right" | 804 || align="right" | 949
|-----
| align="center" | 15-kotniško
| align="center" | ½<i>n</i>(13<i>n</i> - 11)
| align="right" | 1 || align="right" | 15
| align="right" | 42
| align="right" | 82 || align="right" | 135
| align="right" | 201
| align="right" | 280 || align="right" | 372
| align="right" | 477
| align="right" | 595 || align="right" | 726
| align="right" | 870 || align="right" | 1027
|-----
| align="center" | 16-kotniško
| align="center" | ½<i>n</i>(14<i>n</i> - 12)
| align="right" | 1 || align="right" | 16
| align="right" | 45
| align="right" | 88 || align="right" | 145
| align="right" | 216
| align="right" | 301 || align="right" | 400
| align="right" | 513
| align="right" | 640 || align="right" | 781
| align="right" | 936 || align="right" | 1105
|-----
| align="center" | 17-kotniško
| align="center" | ½<i>n</i>(15<i>n</i> - 13)
| align="right" | 1 || align="right" | 17
| align="right" | 48
| align="right" | 94 || align="right" | 155
| align="right" | 231
| align="right" | 322 || align="right" | 428
| align="right" | 549
| align="right" | 685 || align="right" | 836
| align="right" | 1002 || align="right" | 1183
|-----
| align="center" | 18-kotniško
| align="center" | ½<i>n</i>(16<i>n</i> - 14)
| align="right" | 1 || align="right" | 18
| align="right" | 51
| align="right" | 100 || align="right" | 165
| align="right" | 246
| align="right" | 343 || align="right" | 456
| align="right" | 585
| align="right" | 730 || align="right" | 891
| align="right" | 1068 || align="right" | 1261
|-----
| align="center" | 19-kotniško
| align="center" | ½<i>n</i>(17<i>n</i> - 15)
| align="right" | 1 || align="right" | 19
| align="right" | 54
| align="right" | 106 || align="right" | 175
| align="right" | 261
| align="right" | 364 || align="right" | 484
| align="right" | 621
| align="right" | 775 || align="right" | 946
| align="right" | 1134 || align="right" | 1339
|-----
| align="center" | 20-kotniško
| align="center" | ½<i>n</i>(18<i>n</i> - 16)
| align="right" | 1 || align="right" | 20
| align="right" | 57
| align="right" | 112 || align="right" | 185
| align="right" | 276
| align="right" | 385 || align="right" | 512
| align="right" | 657
| align="right" | 820 || align="right" | 1001
| align="right" | 1200 || align="right" | 1417
|-----
| align="center" | 21-kotniško
| align="center" | ½<i>n</i>(19<i>n</i> - 17)
| align="right" | 1 || align="right" | 21
| align="right" | 60
| align="right" | 118 || align="right" | 195
| align="right" | 291
| align="right" | 406 || align="right" | 540
| align="right" | 693
| align="right" | 865 || align="right" | 1056
| align="right" | 1266 || align="right" | 1495
|-----
| align="center" | 22-kotniško
| align="center" | ½<i>n</i>(20<i>n</i> - 18)
| align="right" | 1 || align="right" | 22
| align="right" | 63
| align="right" | 124 || align="right" | 205
| align="right" | 306
| align="right" | 427 || align="right" | 568
| align="right" | 729
| align="right" | 910 || align="right" | 1111
| align="right" | 1332 || align="right" | 1573
|-----
| align="center" | 23-kotniško
| align="center" | ½<i>n</i>(21<i>n</i> - 19)
| align="right" | 1 || align="right" | 23
| align="right" | 66
| align="right" | 130 || align="right" | 215
| align="right" | 321
| align="right" | 448 || align="right" | 596
| align="right" | 765
| align="right" | 955 || align="right" | 1166
| align="right" | 1398 || align="right" | 1651
|-----
| align="center" | 24-kotniško
| align="center" | ½<i>n</i>(22<i>n</i> - 20)
| align="right" | 1 || align="right" | 24
| align="right" | 69
| align="right" | 136 || align="right" | 225
| align="right" | 336
| align="right" | 469 || align="right" | 624
| align="right" | 801
| align="right" | 1000 || align="right" | 1221
| align="right" | 1464 || align="right" | 1729
|-----
| align="center" | 25-kotniško
| align="center" | ½<i>n</i>(23<i>n</i> - 21)
| align="right" | 1 || align="right" | 25
| align="right" | 72
| align="right" | 142 || align="right" | 235
| align="right" | 351
| align="right" | 490 || align="right" | 652
| align="right" | 837
| align="right" | 1045 || align="right" | 1276
| align="right" | 1530 || align="right" | 1807
|-----
| align="center" | 26-kotniško
| align="center" | ½<i>n</i>(24<i>n</i> - 22)
| align="right" | 1 || align="right" | 26
| align="right" | 75
| align="right" | 148 || align="right" | 245
| align="right" | 366
| align="right" | 511 || align="right" | 680
| align="right" | 873
| align="right" | 1090 || align="right" | 1331
| align="right" | 1596 || align="right" | 1885
|-----
| align="center" | 27-kotniško
| align="center" | ½<i>n</i>(25<i>n</i> - 23)
| align="right" | 1 || align="right" | 27
| align="right" | 78
| align="right" | 154 || align="right" | 255
| align="right" | 381
| align="right" | 532 || align="right" | 708
| align="right" | 909
| align="right" | 1135 || align="right" | 1386
| align="right" | 1662 || align="right" | 1963
|-----
| align="center" | 28-kotniško
| align="center" | ½<i>n</i>(26<i>n</i> - 24)
| align="right" | 1 || align="right" | 28
| align="right" | 81
| align="right" | 160 || align="right" | 265
| align="right" | 396
| align="right" | 553 || align="right" | 736
| align="right" | 945
| align="right" | 1180 || align="right" | 1441
| align="right" | 1728 || align="right" | 2041
|-----
| align="center" | 29-kotniško
| align="center" | ½<i>n</i>(27<i>n</i> - 25)
| align="right" | 1 || align="right" | 29
| align="right" | 84
| align="right" | 166 || align="right" | 275
| align="right" | 411
| align="right" | 574 || align="right" | 764
| align="right" | 981
| align="right" | 1225 || align="right" | 1496
| align="right" | 1794 || align="right" | 2119
|-----
| align="center" | 30-kotniško
| align="center" | ½<i>n</i>(28<i>n</i> - 26)
| align="right" | 1 || align="right" | 30
| align="right" | 87
| align="right" | 172 || align="right" | 285
| align="right" | 426
| align="right" | 595 || align="right" | 792
| align="right" | 1017
| align="right" | 1270 || align="right" | 1551
| align="right" | 1860 || align="right" | 2197
|}


== Glej tudi ==
== Glej tudi ==

Redakcija: 14:58, 5. maj 2005

Mnogokótniško števílo je v matematiki število, ki ga lahko razmestimo v obliki pravilnega mnogokotnika. Antični matematiki so ugotovili, da lahko števila razvrstimo na posebne načine, če si jih zamislimo kot kamenčke ali semena. Na primer število 10 lahko razmestimo v obliko trikotnika (glej trikotniško število):

   x 
  x x 
 x x x 
x x x x 

Števila 10 ne moremo postaviti v obliki kvadrata. Na drugi strani lahko tako postavimo število 9 (glej kvadratno število):

x x x 
x x x 
x x x 

Nekatera števila, kot na primer 36, lahko razporedimo kot kvadrat ali kot trikotnik (glej trikotniško kvadratno število):

  x x x x x x 
  x x x x x x 
  x x x x x x 
  x x x x x x 
  x x x x x x 
  x x x x x x 
       x 
      x x 
     x x x 
    x x x x 
   x x x x x 
  x x x x x x 
 x x x x x x x 
x x x x x x x x 

Neko mnogokotniško število povečamo s tem, da razširimo dve sosednji roki za eno točko in med točkami dodamo željeno število strani. Na naslednjih skicah, dodatni nivo prikažemo z znakom +.

Trikotniška števila

1:

+               x

3:

 x               x
+ +             x x

6:

  x               x
 x x             x x
+ + +           x x x

10:

   x               x
  x x             x x
 x x x           x x x
+ + + +         x x x x

Kvadratna števila

1:

+               x

4:

x +             x x
+ +             x x

9:

x x +           x x x
x x +           x x x
+ + +           x x x

16:

x x x +         x x x x
x x x +         x x x x
x x x +         x x x x
+ + + +         x x x x

Tudi mnogokotnike z večjim številom stranic, kot so peterokotniki ali šesterokotniki lahko predstavimo kot razvrstitve točk. Po dogovoru je 1 prvo mnogokotniško število za poljubno število stranic:

Peterokotniška števila

1:

+                   x

5:

 x                   x
+ +                 x x 
+ +                 x x 

12:

   x                   x
  x x                 x x
+ x x +             x x x x
+     +             x     x
+  +  +             x  x  x 

22:

     x                   x
    x x                 x x
  x x x x             x x x x
+ x     x +         x x     x x
+ x  x  x +         x x  x  x x
+         +         x         x
+  +   +  +         x  x   x  x

35:

       x                   x
      x x                 x x
    x x x x             x x x x
  x x     x x         x x     x x 
+ x x  x  x x +     x x x  x  x x x
+ x         x +     x x         x x
+ x  x   x  x +     x x  x   x  x x
+             +     x             x
+  +   +   +  +     x  x   x   x  x


Šesterokotniška števila

1:

 x

6:

    x               x  
  +   +           x   x 
  +   +           x   x 
    +               x  

15:

     x                 x   
   x   x             x   x  
 + x   x +         x x   x x 
 +   x   +         x   x   x 
 +       +         x       x 
   +   +             x   x  
     +                 x   

28:

        x                       x    
      x   x                   x   x   
    x x   x x               x x   x x  
  + x   x   x +           x x   x   x x 
  + x       x +           x x       x x 
  +   x   x   +           x   x   x   x 
  +     x     +           x     x     x 
    +       +               x       x  
      +   +                   x   x   
        +                       x    

45:

          x                           x
        x   x                       x   x    
      x x   x x                   x x   x x   
    x x   x   x x               x x   x   x x  
  + x x       x x +           x x x       x x x 
  + x   x   x   x +           x x   x   x   x x 
  + x     x     x +           x x     x     x x 
  +   x       x   +           x   x       x   x 
  +     x   x     +           x     x   x     x 
    +     x     +               x     x     x  
      +       +                   x       x   
        +   +                       x   x    
          +                           x     

66:

          x                             x
        x   x                         x   x
      x x   x x                     x x   x x
    x x   x   x x                 x x   x   x x
  x x x       x x x             x x x       x x x
+ x x   x   x   x x +         x x x   x   x   x x x
+ x x     x     x x +         x x x     x     x x x
+ x   x       x   x +         x x   x       x   x x
+ x     x   x     x +         x x     x   x     x x
+   x     x     x   +         x   x     x     x   x
+     x       x     +         x     x       x     x
  +     x   x     +             x     x   x     x
    +     x     +                 x     x     x
      +       +                     x       x
        +   +                         x   x
          +                             x

91:

            x                             x
          x   x                         x   x
        x x   x x                     x x   x x
      x x   x   x x                 x x   x   x x
    x x x       x x x             x x x       x x x
  x x x   x   x   x x x         x x x   x   x   x x x
+ x x x     x     x x x +     x x x x     x     x x x x
+ x x   x       x   x x +     x x x   x       x   x x x
+ x x     x   x     x x +     x x x     x   x     x x x
+ x   x     x     x   x +     x x   x     x     x   x x
+ x     x       x     x +     x x     x       x     x x
+   x     x   x     x   +     x   x     x   x     x   x
+     x     x     x     +     x     x     x     x     x
  +     x       x     +         x     x       x     x
    +     x   x     +             x     x   x     x
      +     x     +                 x     x     x
        +       +                     x       x
          +   +                         x   x
            +                             x

Če je s število stranic mnogokotnika, je enačba za n-to s-mnogokotniško število (n/2) ((s-2)n - (4-s)).

Ime Enačba n=1 2 3 4 5 6 7 8 9 10 11 12 13
Trikotniško ½n(1n + 1) 1 3 6 10 15 21 28 36 45 55 66 78 91
Kvadratno ½n(2n - 0) 1 4 9 16 25 36 49 64 81 100 121 144 169
Peterokotniško ½n(3n - 1) 1 5 12 22 35 51 70 92 117 145 176 210 247
Šesterokotniško ½n(4n - 2) 1 6 15 28 45 66 91 120 153 190 231 276 325
Sedmerokotniško ½n(5n - 3) 1 7 18 34 55 81 112 148 189 235 286 342 403
Osmerokotniško ½n(6n - 4) 1 8 21 40 65 96 133 176 225 280 341 408 481
Deveterokotniško ½n(7n - 5) 1 9 24 46 75 111 154 204 261 325 396 474 559
Deseterokotniško ½n(8n - 6) 1 10 27 52 85 126 175 232 297 370 451 540 637
11-kotniško ½n(9n - 7) 1 11 30 58 95 141 196 260 333 415 506 606 715
12-kotniško ½n(10n - 8) 1 12 33 64 105 156 217 288 369 460 561 672 793
13-kotniško ½n(11n - 9) 1 13 36 70 115 171 238 316 405 505 616 738 871
14-kotniško ½n(12n - 10) 1 14 39 76 125 186 259 344 441 550 671 804 949
15-kotniško ½n(13n - 11) 1 15 42 82 135 201 280 372 477 595 726 870 1027
16-kotniško ½n(14n - 12) 1 16 45 88 145 216 301 400 513 640 781 936 1105
17-kotniško ½n(15n - 13) 1 17 48 94 155 231 322 428 549 685 836 1002 1183
18-kotniško ½n(16n - 14) 1 18 51 100 165 246 343 456 585 730 891 1068 1261
19-kotniško ½n(17n - 15) 1 19 54 106 175 261 364 484 621 775 946 1134 1339
20-kotniško ½n(18n - 16) 1 20 57 112 185 276 385 512 657 820 1001 1200 1417
21-kotniško ½n(19n - 17) 1 21 60 118 195 291 406 540 693 865 1056 1266 1495
22-kotniško ½n(20n - 18) 1 22 63 124 205 306 427 568 729 910 1111 1332 1573
23-kotniško ½n(21n - 19) 1 23 66 130 215 321 448 596 765 955 1166 1398 1651
24-kotniško ½n(22n - 20) 1 24 69 136 225 336 469 624 801 1000 1221 1464 1729
25-kotniško ½n(23n - 21) 1 25 72 142 235 351 490 652 837 1045 1276 1530 1807
26-kotniško ½n(24n - 22) 1 26 75 148 245 366 511 680 873 1090 1331 1596 1885
27-kotniško ½n(25n - 23) 1 27 78 154 255 381 532 708 909 1135 1386 1662 1963
28-kotniško ½n(26n - 24) 1 28 81 160 265 396 553 736 945 1180 1441 1728 2041
29-kotniško ½n(27n - 25) 1 29 84 166 275 411 574 764 981 1225 1496 1794 2119
30-kotniško ½n(28n - 26) 1 30 87 172 285 426 595 792 1017 1270 1551 1860 2197

Glej tudi

Vir

  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers, (Penguin Books, 1997) [ISBN 0140261494].

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