Phsicl Secuit Countemesues This entie sheet Telmo, AHI I m going to put heptdecgon into gme. Cssie Hung Mechnicl lockpicking is mechnicked geometic constuctions with compss nd stightedge. Ech lock will hve geometic figue ou must econstuct to open the lock. Equipment fo lockpicking is phsepped compss nd stightedge. The GMs will suppl them, ut ou m ing ou own. You should lso ing pd of ppe. With ou compss nd stightedge, ou m: - Use the compss to dw cs. - Use the compss to mk off distnces. - Use the stightedge to mke stight lines. You m not: - Use ou stightedge s ule. - Use lined ppe fo ou constuctions. - Guess n ngle. - Guess distnce o loction. In genel, if ou wnt to put the little point end of the compss down on the ppe, unless it s the fist stoke of the figue, ou need to put it down on pencil line o intesection. Likewise, if ou wnt to dw stight line, it s usull going to e stight line etween two points. Es locks should e stightfowd fom the emples elow. Moe difficult locks m equie some thinking nd/o sevel steps. Most geometic constuctions cn e solved in multiple ws, usull with tde-off etween compleit of constuction nd thinking, ut in genel if ou know one solution it is d ide to t to find ette one duing mission. Element opetions You should e le to do these ve well. Coping segment: Adding/sutcting segments: - + Phsicl Secuit Countemesues 1 Not Tnsfele
Coping n ngle: Adding/sutcting ngles: + - Bisecting segment/constucting pependicul line: Bisecting n ngle: Angle of 60 : 60 Othe common ngles include 30 (= 60 / 2) nd 45 (= 90 / 2). Line pllel to line though given point: Phsicl Secuit Countemesues 2 Not Tnsfele
Tingles You should e le to do these well. Given 2 ngles nd common side: Given 2 sides nd common ngle: Given 3 sides: z z Isosceles tingle (two sides / two ngles of sme size): Regul polgons You should e le to do these. Hegon: Pentgon: Phsicl Secuit Countemesues 3 Not Tnsfele
Othe opetions You m wnt to undestnd these if ou need to impovise. Ac given chod nd inscied ngle: Cicumcicle of given tingle (fo the cente of given cicle, just mk 3 points on it nd use this): Segment of size 2 + 2 : uild ectngul tingle with cthetus nd nd tke the hpothenuse. Othe tingles Constuctions povided fo infomtive pupose; ou e not likel to need these. Given 2 sides nd non-common ngle (note tht thee e 2 solutions): Given 2 ngles nd othe side (note tht thee is diffeent solution if ou switch the sides): Phsicl Secuit Countemesues 4 Not Tnsfele
Hilious Femt-pime-elted Constuctions (Imge fom http://isoltium.uhh.hwii.edu/m198/w4/17gon.gif, instuctions fom http://mthwold.wolfm.com/heptdecgon.htm The following elegnt constuction fo the heptdecgon (Ytes 1949, Coete 1969, Stewt 1977, Wells 1991) ws fist given Richmond (1893). 1. Given n it point O, dw cicle centeed on O nd dimete dwn though O. 2. Cll the ight end of the dimete dividing the cicle into semicicle P 1. 3. Constuct the dimete pependicul to the oiginl dimete finding the pependicul isecto OB. 4. Constuct J qute of the w up OB. 5. Join JP 1 nd find E so tht OJE is qute of OJP 1. 6. Find F so tht EJF is 45 degees. 7. Constuct the semicicle with dimete FP 1. 8. This semicicle cuts OB t K. 9. Dw semicicle with cente E nd dius EK. 10. This cuts the line segment OP 1 t N 4. 11. Constuct line pependicul to OP 1 though N 4. 12. This line meets the oiginl semicicle t P 4. 13. You now hve points P 1 nd P 4 of heptdecgon. 14. Use P 1 nd P 4 to get the emining 15 points of the heptdecgon ound the oiginl cicle constucting P 1, P 4, P 7, P 10, P 13, P 16 [filled cicles], P 2, P 5, P 8, P 11, P 14, P 17 [single-inged filled cicles], P 3, P 6, P 9, P 12, nd P 15 [doule-inged filled cicles]. 15. Connect the djcent points P i fo i=1 to 17, foming the heptdecgon. Phsicl Secuit Countemesues 5 Not Tnsfele