Read e-book online Machine proofs in geometry : automated production of PDF

By Shang-Ching Chou; Xiao-Shan Gao; Jingzhong Zhang

ISBN-10: 9810215843

ISBN-13: 9789810215842

This quantity includes a suite of twenty written types of invited in addition to contributed papers awarded on the convention held from 20-24 may perhaps 1996 in Beijing, China. It covers many components of good judgment and the rules of arithmetic, in addition to desktop technology. additionally incorporated is a piece of writing via M. Yasugi at the Asian common sense convention which first seemed in eastern, to supply a glimpse into the background and improvement of the sequence Pt. I. the speculation of desktop evidence. 1. Geometry Preliminaries. 2. the realm procedure. three. computer facts in airplane Geometry. four. computing device evidence in stable Geometry. five. Vectors and computing device Proofs -- Pt. II. subject matters From Geometry: a set of four hundred routinely Proved Theorems. 6. themes From Geometry

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Additional info for Machine proofs in geometry : automated production of readable proofs for geometry theorems

Example text

SBDA P AOB PAOBSACD = PAOC SACD P AOB . BD CD = P AOC . PAO B P AOB PAoc = l. 69 On the two sides AB and AC of triangle ABC, two squares ABDE and ACFG are drawn externally. CE. 70 In triangle ABC, take a point J on the altitudes AD. Lines BJ and CJ meet AC and AB in N and M respectively. Show that LM DA = LADN. 56 we need only to show PMDA/SMDA Figure 1-45 = PADN/SADN .

Cos(t(AC, DB»2 = 1, we have 4S~BCD AC2. ,-=2 = 4AC -2 2 P~BCD + 4AC2. BD2 = 1. BD - PABCD ' Chapter 1. 90 1. 80 to prove the following fonnulas sin(a - 13) cos(a + 13 ) cos(a - 13) 2. Let tan( a) = = sine a) cos(f3) - cos( a) sin(f3) sine a) sin(f3) - cos( a) cos(f3) sine a) sin(f3) + cos( a) cos(f3) = ;~:~:l . Show that tan (a tan( a) + tan(f3) tan () a tan () 13 , + 13 ) = 1 - 13 tan( a - tan( a) - tan(f3) ) = 1 + tan( a) tan(f3)" 3. Prove the following version of the Herron-Qin fonnula for quadrilaterals.

1'LABC > LXY Z and LABC + LXY Z > 180° then 'J 2• (The Converse of the Co-angle Theorem) /£ 'J LXY Z or LABC + LXY Z = 180°. 45 In triangle ABC, if LB > P roo),£. By the co-angle 'mequ al'lty, 1 -- LC then AC 'jZABC \7ACB > 'jZABC \7XYZ 'jZABC \7XYZ = < AB·BC XY·YZ· AB·B C XY ·YZ then LABC = > AB. BC - .. 46 1. Among the segments from a point to any point on a line, the perpendicular is the shortest. I 2. The area of any quadrilateral is less than or equal to half of the products of its two diagonals.

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Machine proofs in geometry : automated production of readable proofs for geometry theorems by Shang-Ching Chou; Xiao-Shan Gao; Jingzhong Zhang

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