Madrid PAU Technical Drawing Applied to Arts and Design II flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thales' theorem

An angle inscribed in a semicircle is a right angle; conversely, the circumcenter of a right triangle is the midpoint of its hypotenuse.

Golden ratio

The ratio φ = (1+√5)/2 ≈ 1.618, obtained when a segment is divided so that the whole is to the larger part as the larger is to the smaller.

Power of a point

For a point P at distance d from the center of a circle of radius r, the power is d² − r²; the tangent length from P equals the square root of the power.

Radical axis

The line formed by all points that have equal power with respect to two given circles; it is perpendicular to the line joining their centers.

Homothety

A transformation with center O and ratio k that maps each point P to P' on line OP such that OP' = k·OP; it preserves angles and maps circles to circles.

Similarity transformation

A composition of a homothety and an isometry; it preserves shape and angles while multiplying all lengths by a constant factor.

Inversion in a circle

A transformation that maps point P to P' on ray OP such that OP·OP' = r², where r is the radius of the inversion circle centered at O.

Inversion of a line

A line not passing through the inversion center maps to a circle through the center; a line through the center maps to itself.

Composition of homotheties

Two homotheties with centers O₁ and O₂ and ratios k₁ and k₂ compose to a homothety of ratio k₁k₂ (if k₁k₂ ≠ 1) whose center lies on line O₁O₂.

Tangency of two circles

Two circles are tangent when the distance between their centers equals the sum of their radii (external tangency) or the absolute difference (internal tangency).

Ellipse definition

The locus of points whose sum of distances to two fixed foci is constant 2a; the major axis is 2a and the minor axis is 2b with a² = b² + c².

Parabola definition

The locus of points equidistant from a fixed focus and a fixed directrix; in standard form y² = 2px, where p is the focus-to-directrix distance.

Hyperbola definition

The locus of points for which the absolute difference of distances to two foci is constant 2a; its asymptotes have slopes ±b/a and eccentricity e = c/a > 1.

Involute curve

The path traced by a point on a taut string unwinding from a circle; it is the standard profile for gear teeth because it gives conjugate action.

Monge projection

A descriptive geometry method representing a point by its horizontal (plan) and vertical (elevation) projections on two perpendicular planes separated by the ground line.

True length by right triangle

The true length of a segment equals the hypotenuse of a right triangle whose legs are the segment's projection and its height difference (or depth difference).

Edge-view of a line

The projection that shows a line as a point; it is obtained by viewing along the line direction and is used to find true angles and distances.

Plane traces

The lines where a plane intersects the horizontal and vertical projection planes; they define the plane in Monge projection.

Euler's formula

For any convex polyhedron, V − E + F = 2, where V is the number of vertices, E the number of edges, and F the number of faces.

Platonic solids

The five regular convex polyhedra: tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), dodecahedron (12 pentagons), icosahedron (20 triangles).

Cone lateral area

The lateral surface area of a right cone is πrl, where r is the base radius and l the slant height; l² = r² + h² with height h.

Developable surface

A surface that can be flattened onto a plane without stretching or tearing; cylinders and cones are developable, while spheres are not.

First-angle projection

A projection method in which the object lies between the observer and the projection plane; the top view is placed below the front view in the layout.

Third-angle projection

A projection method in which the projection plane lies between the observer and the object; the top view is placed above the front view.

ISO dimensioning rules

Dimension lines are parallel to the measured direction with arrowheads at both ends; extension lines start with a small gap from the object; each dimension is given once.

ISO line types

Continuous thick lines show visible edges; continuous thin lines show dimensions and extension lines; dashed lines show hidden edges; chain lines show center lines.

Clearance fit

A fit in which the hole tolerance zone lies entirely above the shaft tolerance zone, so there is always a gap between the mating parts.

Isometric projection

An axonometric projection with three axes at 120° and equal foreshortening along all three; true isometric scale is about 0.816 of full scale.

Cabinet projection

An oblique projection in which the front face is shown true shape and the receding axis is drawn at 45° with half scale.

Two-point perspective

A perspective in which vertical edges remain parallel to the picture plane and two vanishing points lie on the horizon line for the two horizontal directions.

Measuring points method

A perspective construction technique that uses measuring points on the horizon line to transfer true lengths along receding axes.

Line weight hierarchy

In presentation drawings, thick lines outline visible edges, medium lines show internal edges, and thin lines are used for construction and dimensioning.