# Plane and Solid Geometry: Concepts and Tools

### Plane geometry:

part of the **geometry** that considers the figures whose points are all on a **plane**.**Geometry of space,** which considers the figures whose points are not all on the same plane.

### Descriptive geometry:

that is to resolve problems the geometry of space by means of cash transactions in a plane and it figures represent solids.

### Projective geometry:

that is the projection of figures on a plane.

### Analytic geometry:

a study of figures which uses a coordinate system and methods of mathematical analysis. **Section conical** intersection curve of a cone with a plane not passing through its apex. They are classified into three types: ellipse, parabola, and hyperbola. The **hyperboloid** is the surface of revolution generated by rotating a hyperbola about one of its two axes. **Hyperbola** is the locus of points on the plane for which the difference of distances to two fixed points called foci, is constant and less than that distance between the foci. **Ellipse** is the locus of points in the plane such that the sum of the distances to two fixed points called foci is constant. **Parabola** is the locus of points in the plane which are equidistant from a fixed **point** called the focus, and a **line** called guideline.

### Straight:

continuous and indefinite succession of points in a single dimension. **Ray** is becoming one of the two parts into which a line is divided by any of its points. **Point** is a dimensionless geometric element is not a physical object, describes a position in space, determined according to a predetermined coordinate system. **Prism** is a polyhedron consisting of two equal and parallel faces called bases, and lateral faces are parallelograms.

### Poliedro:

solid figure whose faces are flat and contain a finite volume.

### Polyhedra:

it is one in which it is verified that any pair of points located inside the line segment joining a well inside. **polygon** is a geometric figure formed by consecutive non-aligned segments, called sides shape of its outline, is called: **simple** if two nonconsecutive edges do not intersect (cut); **complex** if two non-consecutive edges intersect; **convex** if a line passing through it is cut into a maximum of two points; **concave** if the line can cross a cut in more than two points, **regular** if it has its angles and its sides are equal, if you have **irregular** angles and uneven sides, **equilateral** which has all its sides equal, **equiangular** which has all its angles equal . Cuboid polyhedron of six faces (and therefore a hexahedron), in which all faces are parallelograms, and parallel and equal in pairs.

### Polygon line:

ordered set of segments such that the end of one of them coincides with the origin segment that follows. A **polygon** is formed by a closed polygonal line. **Bisector** of a segment is the line drawn perpendicular to this segment at its midpoint. Parallelepiped is a polyhedron of six faces (therefore, a hexahedron), in which all faces are parallelograms, and parallel and equal in pairs. **bisector** of an **angle** is the line that divides it into two equal parts, locus of equidistant points on the plane (they are at the same distance) from the rays of an angle. **generatrix** is a line because of their movement as a geometric figure, which in turn depends on the guideline. The generating can be a **straight** line or curve: curves generated by generating circumferences: **Cycloid,** the plane curve generated by a point of a generating circle to roll on a straight line without slipping. **Epicycloid,** the curve that describes a point related to a generating circle which rolls without slipping-on-one guidance circle tangentially. **Hypocycloid,** the curve that describes the path a point on a generating circle that rolls inside another circle guideline, without slipping. **trochoid,** flat curve describes a point, linked to a generating circle, which rolls on a straight line guideline, tangentially, without slipping. **Epitrochoid,** the curve that describes a point linked to a generating circle which rolls without slipping-on-one guidance circle tangentially.

### Hypotrochoid

The plane curve that describes a point linked to a generating circle that rolls within a circle guideline, tangentially, without slipping. **Plan** is the ideal entity that has only two dimensions, and contains infinite points and lines. **half plane** each of the two parts into which a plane is divided by a line. **Isometric** is a graphic method of representation, specifically a cylindrical orthogonal axonometric. **caballera Vista** is a system of oblique parallel projection, where the dimensions of the front projecting plane, like those of elements parallel to him are true magnitude. **Conic** graphic representation system where the projecting beam converges at a point (the eye of the observer), projecting the image in an auxiliary plane located between the object and point to represent of view.

### Axonometric perspective:

is a graphical representation system, consisting of geometric elements representing or volumes on a plane, with orthogonal projection, referred to three orthogonal axes, so that they retain their proportions in the three spatial directions: height, width and length of the conical **differs** because the scale of the represented object does not depend on its distance from the observer (equivalent to the observer were at infinity). Two parallel lines are also parallel reality in axonometric representation.

### Orthogonal projection:

is one whose projecting auxiliary lines are perpendicular to the plane of projection, establishing a relationship between all points of the projected projecting element. **Vertex** is the point where they attend the two rays that form an angle. **angle** of the plane are part between two rays which have the same origen.Suelen measured in units such as the radian, degree sexagesimal or grad dihedral angle is called the space between two half-planes whose common origin is a straight line. A solid angle is covered by an object seen from a given point by measuring its apparent size. **Circumcenter** is the point of intersection of the three bisectors of a **triangle** and is the center of the circumcircle.Sphere is a solid body bounded by a curved surface whose points are equidistant from an inner called the center of the sphere. **Cone** is a solid of revolution generated by rotating a right triangle about one of its legs. **Cylinder** surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. As a surface of revolution is obtained by rotating a line around another fixed axis of revolution called. **Triangle** is a polygon determined by three straight to cut two to two in three points (which are not aligned). **Compass** instrument used to draw circles or arcs of circumference. It comprises two *legs* joined by a hinge, the opening can be adjusted easily. Generally, a leg with a needle and the other a mine or an adapter for pencils, markers or ink pens. The upper end has a hollow cylinder to grasp it and facilitate the movement of rotation, **there are** four types of time these are mine Compass stroke or **stroke The compass** has two adjustable legs with pointed toes of iron and one in mine . One end of the bar has a mine to make the strokes and the other has a punch to keep the instrument fixed on the sheet of paper. **Bigotera Compass** maintain fixed is characterized by the radius of aperture, who graduates with a screw or threaded shaft with pinpoint accuracy. It is used to draw small circles and circles of equal radius. **Ballerina or crazy mustache** is a special **compass** for drawing circles very small radius. **Compass golden** compass is a three-pronged for dividing a line in extreme and mean ratio . A **carrier** is an instrument for measuring angles in degrees that comes in two basic: **Conveyor with a semicircular** graduated in 180 degrees (sexagesimal degrees) or 200 ^{g} (grads). **Conveyor with a circular graduated** in 360 ° or 400.

### Squad:

Established form of right triangle that is used in technical drawing, p Osee an angle of 90 ° and two 45-second, often used with a **yardstick or ruler** to draw parallel and perpendicular lines. **Bevel** is a template form of scalene triangle that is used in design. They can be different sizes and have a graphic scale, for use as a measuring tool. It has the shape of a triangle whose angles are 90 º, 60 º and 30 º. Often used, along with a square or a ruler to draw lines parallel or perpendicular angles. We use the yardstick to: Draw parallel to any preset distance. Draw perpendicular. Check the angle measures. Get the polar coordinates. Quickly locate the midpoint. Getting the symmetry of plane figures. Get vector measures. Get angles of 30 º and 60 º. Draw triangles. **Rule** is a measuring instrument with a thin rectangular plate that includes a scale divided into units of length, eg cm or inches. **Pencil** is a writing or drawing instrument consisting of a thin stick of pigment ( usually grease or graphite and a special clay, but can also be colored pigment charcoal) and usually encapsulated in a thin wood cylinder, though paper and plastic wraps are also used.Dial Indicators is a special rule which has a prismatic cross section in order to contain different scales on the same rule. It is used to measure in drawings that contain a variety of scales. At its edge contains a range with calibrated scales and simply rotate about its longitudinal axis to view the appropriate level. **Stylus** is a tool for technical drawing and writing, containing a liquid ink reservoir consists primarily of water. The ink remains in the tank due to atmospheric pressure until it is used, the ink fed to the *nib,* the final metal part, through a channel by the combination of gravity and capillarity. To fill the tank there are several methods, including replacing the tank on the other, complete with a dropper or suck the ink from an inkwell.