If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces which can be reassembled to form the second polygon.

## If that polygon is wholly in front of the plane containing P, move that polygon to the list of nodes in front of P.

## If that polygon is wholly behind the plane containing P, move that polygon to the list of nodes behind P.

## If that polygon is intersected by the plane containing P, split it into two polygons and move them to the respective lists of polygons behind and in front of P.

## If that polygon lies in the plane containing P, add it to the list of polygons at node N.

If the area is sufficiently large, the polygon will not close no matter how accurately measured if it is calculated on a plane.

If the path is a simple path, with no repeated vertices or edges other than the starting and ending vertices, it may also be called a simple cycle, circuit, circle, or polygon ; see Cycle graph.

If it is even, the point lies outside the polygon ; this test also works in three dimensions.

If the point in question is not on the boundary of the polygon, the number of intersections is an even number if the point is outside, and it is odd if inside.

If the ray passes exactly through a vertex of a polygon, then it will intersect 2 segments at their endpoints.

The issue is solved as follows: If the intersection point is a vertex of a tested polygon side, then the intersection counts only if the second vertex of the side lies below the ray.

If the polygon is specified by its vertices, then this problem is eliminated by checking the y-coordinates of the ray and the ends of the tested polygon side before actual computation of the intersection.

If the winding number is non-zero, the point lies inside the polygon.

If every internal angle of a simple, closed polygon is less than 180 °, the polygon is called convex.

If the corners of a polygon of size n are all connected to one another, the number of intersections created will be a pentatope number.

If the sides intersect then the polygon is not simple.

If a closed polygonal chain embedded in the plane divides it into two regions one of which is topologically equivalent to a disk, then the chain is called a weakly simple polygon.

If the angle ( rotation ) at which the symmetry occurs divides evenly into a full circle ( 360 °), the result is the helical equivalent of a regular polygon.

If the sequence is correctly constructed, the difference in area between the n-th polygon and the containing shape will become arbitrarily small as n becomes large.

If normal mapping is used, each polygon has many face normals ( the direction a given point on a polygon is facing ), which can be used in tandem with an environment map to produce a more realistic reflection.

If any of us miss, they can pick up the pieces.

`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.

If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If Mrs. Wright doesn't accept the terms in the morning, I'll go either to Tokyo or to Holland, to do what I can.

If within one year you can make a success out of the American, you can practically name your own salary thereafter.

If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.

If there be a disinterested patriot in America, 'tis General Washington, and his bravery, none can question ''.

`` If you can firmly make the good knight sure to pleasure our Corporation '', Sturley wrote, `` besides that ordinary allowance for your diet you shall have 20 for recompence ''.

If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.

If the manner of his passing moves the nations to act in the spirit of his dedication the sore issues that plague the world can yet be resolved with reason and justice.

If they do as well as they did in 1960 there can be no complaint.

If he can bounce back with one of those 25 home runs years, the club will have to be better off offensively.

If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.

`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.

If we cluster together, the redcoats can make an advantage out of it, but there's not a blessed thing they can do with two or three of us except chase us, and we can outrun them ''.

If there is anything which we can do in the executive branch of the Government to speed up the processes by which we come to decisions on matters on which we must act promptly, that in itself would be a major contribution to the conduct of our affairs.

If the target can change its position significantly during the 30 minutes the missile is in the air on its way, the probability of the missile destroying the target is drastically reduced.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

If there are any major restrictions, they usually can be obtained in printed form.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.