Automated Deduction in Geometry: 5th International Workshop, by Laura I. Meikle, Jacques D. Fleuriot (auth.), Hoon Hong,

By Laura I. Meikle, Jacques D. Fleuriot (auth.), Hoon Hong, Dongming Wang (eds.)

This ebook constitutes the completely refereed post-proceedings of the fifth foreign Workshop on automatic Deduction in Geometry, ADG 2004, held at Gainesville, FL, united states in September 2004.

The 12 revised complete papers provided have been conscientiously chosen from the papers permitted for the workshop after cautious reviewing. All present matters within the sector are addressed - theoretical and methodological issues in addition to functions thereof - specifically computerized geometry theorem proving, computerized geometry challenge fixing, difficulties of dynamic geometry, and an object-oriented language for geometric objects.

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Additional info for Automated Deduction in Geometry: 5th International Workshop, ADG 2004, Gainesville, FL, USA, September 16-18, 2004. Revised Papers

Sample text

We will use the formula (4), which is due to Nagy and R´edey [11]. 1 di,j di,j+1 . di+1,j di+1,j+1 (4) Formula of Heron The well-known formula of Heron is a special case of (4). We will derive it by computer. A triangle ABC with sides a, b, c is given. Find the formula for the area p of ABC. Choose the Cartesian coordinate system so that the coordinates of the vertices of a triangle ABC are A = [0, 0], B = [c, 0], C = [x, y], see Fig. 1. We want to express the area p of the triangle ABC by the lengths of its sides a = |BC|, b = |CA|, c = |AB|.

FoldBring[A, B,MarkCrease → {CD, EF}]; Unfold[]; Steps 6-13: Applying four more times axiom (FoldBring) we obtain in order points K, L, crease M N and point O. Computational Origami Construction of a Regular Heptagon FoldBring[D, Unfold[]; FoldBring[C, Unfold[]; FoldBring[L, Unfold[]; FoldBring[A, Unfold[]; 23 H,MarkCrease → {FE}]; H,MarkCrease → {CD}]; H,MarkCrease → {AB, CD}]; F,MarkCrease → {MN}]; 6SHFLI\ WKH OLQH QXPEHU ' ) + 1 / . 2  0 % $ & ' 2 (0 ) )+ 1 / - '  ( *  $ & , + 1 / . * ( 2 % $ 0 6WHS  6WHS  & 4 % 6WHS  6SHFLI\ WKH OLQH QXP ' ' ) .

An important problem concerning proving geometric theorems is to determine whether a geometric statement is valid under a specialization of parameters. In detail, a geometric statement of equality-type consists of two parts: hypotheses and conclusion. Both hypotheses and conclusion can be expressed in terms of polynomial equations in a number of free arbitrary coordinates u1 , . , um , which we call parameters, and a number of dependent coordinates x1 , . . , xn , which we call variables. Typically, the hypotheses are composed of ⎧ ⎨ h1 (u1 , .

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