Machinery's Handbook, 31st Edition
DIAGONALS OF SQUARES AND HEXAGONS 87 Diagonals of Squares and Hexagons.— The table below gives values of dimensions D and E described in the figures and equations that follow.
2 3 3 ----- d
=
=
1.154701 d
D
d
E d 2 1.414214 d = =
A value not given in the table can be obtained from the equations above, or by the simple addition of two or more values taken directly from the table. Further values can be ob- tained by shifting the decimal point. Example 1: Find D when d = 2 5 ⁄ 16 inches. From the table, for d = 2, D = 2.3094, and for d = 5 ⁄ 16 , D = 0.3608. Therefore, D = 2.3094 + 0.3608 = 2.6702 inches. Example 2: Find E when d = 20.25 millimeters. From the table, for d = 20, E = 28.2843; for d = 0.25, that is, 1 ⁄ 4 , E = 0.3536; Thus, E = 28.2843 + 0.3536 = 28.6379 millimeters. Diagonals of Squares and Hexagons (US Customary or Metric Units) d D E d D E d D E d D E 1 ⁄ 32 0.0361 0.0442 0.9 1.0392 1.2728 32 36.9504 45.2548 67 77.3650 94.7523 1 ⁄ 16 0.0722 0.0884 29 ⁄ 32 1.0464 1.2816 33 38.1051 46.6691 68 78.5197 96.1666 3 ⁄ 32 0.1083 0.1326 15 ⁄ 16 1.0825 1.3258 34 39.2598 48.0833 69 79.6744 97.5808 0.1 0.1155 0.1414 31 ⁄ 32 1.1186 1.3700 35 40.4145 49.4975 70 80.8291 98.9950 1 ⁄ 8 0.1443 0.1768 1.0 1.1547 1.4142 36 41.5692 50.9117 71 81.9838 100.409 5 ⁄ 32 0.1804 0.2210 2.0 2.3094 2.8284 37 42.7239 52.3259 72 83.1385 101.823 3 ⁄ 16 0.2165 0.2652 3.0 3.4641 4.2426 38 43.8786 53.7401 73 84.2932 103.238 0.2 0.2309 0.2828 4.0 4.6188 5.6569 39 45.0333 55.1543 74 85.4479 104.652 7 ⁄ 32 0.2526 0.3094 5.0 5.7735 7.0711 40 46.1880 56.5686 75 86.6026 106.066 1 ⁄ 4 0.2887 0.3536 6.0 6.9282 8.4853 41 47.3427 57.9828 76 87.7573 107.480 9 ⁄ 32 0.3248 0.3977 7.0 8.0829 9.8995 42 48.4974 59.3970 77 88.9120 108.894 0.3 0.3464 0.4243 8.0 9.2376 11.3137 43 49.6521 60.8112 78 90.0667 110.309 5 ⁄ 16 0.3608 0.4419 9.0 10.3923 12.7279 44 50.8068 62.2254 79 91.2214 111.723 11 ⁄ 32 0.3969 0.4861 10 11.5470 14.1421 45 51.9615 63.6396 80 92.3761 113.137 3 ⁄ 8 0.4330 0.5303 11 12.7017 15.5564 46 53.1162 65.0538 81 93.5308 114.551 0.4 0.4619 0.5657 12 13.8564 16.9706 47 54.2709 66.4681 82 94.6855 115.966 13 ⁄ 32 0.4691 0.5745 13 15.0111 18.3848 48 55.4256 67.8823 83 95.8402 117.380 7 ⁄ 16 0.5052 0.6187 14 16.1658 19.7990 49 56.5803 69.2965 84 96.9949 118.794 15 ⁄ 32 0.5413 0.6629 15 17.3205 21.2132 50 57.7351 70.7107 85 98.1496 120.208 0.5 0.5774 0.7071 16 18.4752 22.6274 51 58.8898 72.1249 86 99.3043 121.622 17 ⁄ 32 0.6134 0.7513 17 19.6299 24.0416 52 60.0445 73.5391 87 100.459 123.037 9 ⁄ 16 0.6495 0.7955 18 20.7846 25.4559 53 61.1992 74.9533 88 101.614 124.451 19 ⁄ 32 0.6856 0.8397 19 21.9393 26.8701 54 62.3539 76.3676 89 102.768 125.865 0.6 0.6928 0.8485 20 23.0940 28.2843 55 63.5086 77.7818 90 103.923 127.279 5 ⁄ 8 0.7217 0.8839 21 24.2487 29.6985 56 64.6633 79.1960 91 105.078 128.693 21 ⁄ 32 0.7578 0.9281 22 25.4034 31.1127 57 65.8180 80.6102 92 106.232 130.108 11 ⁄ 16 0.7939 0.9723 23 26.5581 32.5269 58 66.9727 82.0244 93 107.387 131.522 0.7 0.8083 0.9899 24 27.7128 33.9411 59 68.1274 83.4386 94 108.542 132.936 23 ⁄ 32 0.8299 1.0165 25 28.8675 35.3554 60 69.2821 84.8528 95 109.697 134.350 3 ⁄ 4 0.8660 1.0607 26 30.0222 36.7696 61 70.4368 86.2671 96 110.851 135.765 25 ⁄ 32 0.9021 1.1049 27 31.1769 38.1838 62 71.5915 87.6813 97 112.006 137.179 0.8 0.9238 1.1314 28 32.3316 39.5980 63 72.7462 89.0955 98 113.161 138.593 13 ⁄ 16 0.9382 1.1490 29 33.4863 41.0122 64 73.9009 90.5097 99 114.315 140.007 27 ⁄ 32 0.9743 1.1932 30 34.6410 42.4264 65 75.0556 91.9239 100 115.470 141.421 7 ⁄ 8 1.0104 1.2374 31 35.7957 43.8406 66 76.2103 93.3381 … … …
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