two
2
The union of two coplanar half-planes along their common edge forms a region that includes both half-planes and their shared boundary line. This region is essentially the entire plane on one side of the edge, encompassing all points in both half-planes. If the half-planes are defined by two lines intersecting at their common edge, the union will include all points on both sides of the edge, effectively covering a larger area.
A half-plane in mathematics refers to one of the two regions into which a plane is divided by a straight line. It consists of all points on one side of the line, including the line itself if it is included in the definition. Mathematically, a half-plane can be described by a linear inequality, such as ( ax + by \leq c ), where ( a ), ( b ), and ( c ) are constants. Half-planes are fundamental in geometry and linear programming, as they represent feasible regions for solutions.
If I understand the grammar correctly, the answer is one line.
To find the planes of symmetry of a cuboid, visualize or draw the shape and identify its dimensions. A cuboid has three planes of symmetry: one that divides it into two equal sections along the length, one along the width, and one along the height. Each plane bisects the cuboid and creates two mirror-image halves. You can confirm symmetry by checking if one half is a mirror reflection of the other across the identified plane.
2
-- A line has no plane and no part of one. -- Regarding a plane, go back and look at that word "half" again.
boundary line
In general no. The intersection of two parallel half-planes A and B is either a half-plane (either A or B, when A and B have similar orientation) or the empty set (when A and B have opposite orientation). When A and B are not parallel, their intersection is a maximal open region bounded by the two lines that define A and B, respectively. In this case, the intersection always exists and it is never a half-plane.
8
Yes, two planes. Each of them divides the seam in half.
The union of two coplanar half-planes along their common edge forms a region that includes both half-planes and their shared boundary line. This region is essentially the entire plane on one side of the edge, encompassing all points in both half-planes. If the half-planes are defined by two lines intersecting at their common edge, the union will include all points on both sides of the edge, effectively covering a larger area.
you fold the paper in half and you fold it verticaly and you fold it verticaly again and you've got your paper plane.
A half-plane in mathematics refers to one of the two regions into which a plane is divided by a straight line. It consists of all points on one side of the line, including the line itself if it is included in the definition. Mathematically, a half-plane can be described by a linear inequality, such as ( ax + by \leq c ), where ( a ), ( b ), and ( c ) are constants. Half-planes are fundamental in geometry and linear programming, as they represent feasible regions for solutions.
If I understand the grammar correctly, the answer is one line.
There are more solutions in a half plane
A cylinder and a cone have infinitely many planes of symmetry because of the circular face. However, a cylinder can also be cut in half lengthwise (imaging cutting a soda can in half), while a cone cannot (imagine cutting a ice cream cone in half). Therefore, a cylinder has one more plane of symmetry than a cone.