### Table 1 Routine procedures and relevant competencies difer from facts, definitions, and algorithmic procedures in that they are somewhat less cut-and-dried. Facts are right or wrong, and algorithms, when aplied corectly, are guaranted to work; routine procedures are likely to work, but with no guarantes. For example, the problem above, although stated as a construction problem, is intimately tied to a prof problem. One neds to know hat properties the desired circle has, and the most direct way of determining them is to prove that in a figure including the circle (see Figure 1), PV and QV are the same length, and CV bisects angle PVQ.

"... In PAGE 46: ... People experienced in the domain know that one should to seek congruent triangles, and that it is apropriate to draw in the line segments CV, CP and CQ; moreover, that one of the standard methods for proving triangles congruent (SS, ASA, AS, or hypotenuse-leg) wil probably be used, and that this knowledge should drive the search process. We note that al of the coments made in the discussion of Table1... ..."

### Table X. Congruent Interface Transcript

1998

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### Table 3. Some main characteristics of constructive research congruent to this study.

"... In PAGE 5: ...able 2. Papers included and their contributions to the study. ............................................49 Table3 .... In PAGE 55: ... Therefore, a system approach is also used. Table3 lists some characteristics of constructive research and presents how these are applied to this study. Table 3.... ..."

### Table 7. The number of pseudoprimes congruent to c modulo m.

13

"... In PAGE 10: ... prime factors. We have P ?1013 = 264239. In Table 2 we give the smallest pseudoprime with d prime factors for d up to 17. In Table7 we give the number of pseudoprimes in each class modulo m for m up to 12. In Tables 8 and 8 we give the number of pseudoprimes divisible by primes p up to 97.... ..."

### Table 2. Ratio of shadow triangles to total triangles

1998

"... In PAGE 8: ... One would expect the number of shadow trian- gles to grow like the square root of the total number of triangles in two dimensional problems [8]. Table2 con- tains the ratio of the number of shadow triangles to the number of triangles in the grid for several grid sizes and 2, 4 and 8 processors for the example problem. The square root relationship is clearly seen.... ..."

Cited by 6

### Table 2. Triangle Counts of Cortex Surfaces Triangle Triangle Savings

### Table 3: The prime factorization of the congruent pairs of Table 2. The en- tries in the table represent the exponents of the corresponding prime factor.

in 1

2002

"... In PAGE 13: ... We do not use the congruent pair (49; 16), because both sides are already squares. From the pairs in Table 2, we now construct another table, Table3 , that contains the prime factorizations of the a and b. From Table 2, take for example the 4th and the 10th pairs.... In PAGE 14: ...From Table3 , we may nd the subsets S0 as follows. Since we have to choose elements in such a way that their product is a square, we have to make sure that the exponent of each prime is even, in a and b together.... ..."

### Table 2. Number of triangles

"... In PAGE 6: ...6 triangles in the 512x512 image. Table2 summarizes the number of triangles subdi- vided and rendered in each AS approach. With the software renderer both adaptive shading methods require less than twice the time of Gouraud shad- ing, and Phong shading requires 7.... ..."

### Table 1: Triangle Counts

"... In PAGE 6: ... We tested bending along the y-axis of the object and measured the amount of subdivision that occurred. The results are summarized in Table1 and are shown in Plate 1. The first two cases show the greatest amount of subdivision since the original mesh is composed of flat Triangle Count... ..."