PAU Technical Drawing II (Aragón) flashcards

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

Circumcentre

Point where the three perpendicular bisectors of a triangle's sides meet; it is equidistant from all three vertices and is the centre of the circumscribed circle.

Incentre

Intersection of the three internal angle bisectors of a triangle; equidistant from the three sides, so it is the centre of the inscribed circle.

Side of regular polygon

For a regular n-gon inscribed in a circle of radius R, the side is s = 2R·sin(180°/n); for a square s = R√2 and for a hexagon s = R.

Cyclic quadrilateral condition

A quadrilateral can be inscribed in a circle exactly when its opposite angles are supplementary, that is, they add up to 180 degrees.

Homothety ratio effects

A homothety of ratio k maps lengths to |k| times their value and areas to k² times; lines map to parallel lines and angles are unchanged.

Inversion of a line

Under inversion centred at O, a line not passing through O maps to a circle through O, and a circle through O maps to a line not through O.

Cross-ratio invariance

Projective transformations map lines to lines and preserve the cross-ratio of four collinear points, though lengths and angles generally change.

Similarity transformation

Composition of a homothety with an isometry; it preserves angles and multiplies every length by one common ratio r, so areas scale by r².

Tangent from external point

Draw the circle with diameter OP, where O is the given circle's centre; its intersections with the given circle are the two tangency points.

Ellipse focal property

For every point of an ellipse the sum of its distances to the two foci equals the major axis 2a; the semi-minor axis satisfies b² = a² − c².

Conic section by plane angle

A plane cutting a cone gives a circle when perpendicular to the axis, an ellipse when oblique, a parabola when parallel to a generatrix, and a hyperbola when parallel to the axis.

Archimedean spiral equation

In polar form r = a + bθ; successive turns are separated by the constant radial distance 2πb, unlike the logarithmic spiral's geometric growth.

Envelope of a line family

The curve tangent to every line of the family; for example, the envelope of the family of normals to a curve is its evolute.

True length by right triangle

A segment's true length is the hypotenuse of a right triangle whose legs are its projection and the difference of its distances to the projection plane.

Line perpendicular to plane

If a line is perpendicular to a plane, its horizontal and vertical projections are each perpendicular to the corresponding trace of that plane.

Line piercing a plane

Pass an auxiliary projecting plane through the line, intersect it with the given plane, and the meeting point of that intersection line with the given line is the piercing point.

True shape by abatement

Rotate the cutting plane about one of its traces until it coincides with the projection plane; the figure then appears in true size and shape.

Cone development sector angle

A right cone of base radius r and slant height g develops into a circular sector of radius g and angle 360°·r/g.

Cylinder development

The lateral surface of a right cylinder of radius r and height h unfolds into a rectangle of width 2πr and height h.

Section of a polyhedron

The section polygon's vertices are the piercing points of the cutting plane with the solid's edges; its sides lie in the faces.

Sphere plane section

Any plane cutting a sphere gives a circle; its true size appears in a view parallel to the cutting plane, with radius √(R² − d²).

ISO A0 format

A0 measures 841 × 1189 mm and has an area of one square metre; each following size halves the larger side, giving A4 = 210 × 297 mm.

Dimension line conventions

Extension lines start about 1 mm from the object and extend roughly 2 mm past the dimension line; the value is written above the line, readable from below or right.

ISO 128 line types

Continuous thick for visible edges, continuous thin for dimensions, dashed for hidden edges, dash-dot thin for centre and symmetry lines.

Scale computation

Real length equals drawing length multiplied by the scale denominator; a 60 mm segment at 1:5 represents 300 mm, and areas scale by the square of the ratio.

First-angle projection layout

The object lies between observer and plane, so the left-side view is placed on the right and the top view is placed below the front view.

Isometric foreshortening

In true isometric projection all three axes foreshorten by 0.816; isometric drawings conventionally use full scale along the axes instead.

Isometric circle ellipse axes

A circle of diameter d appears in isometric view as an ellipse with major axis about 1.22d and minor axis about 0.71d, ratio √3:1.

View dimension correspondence

The front view gives width and height, the top view width and depth, the side view height and depth; depth transfers between top and side views.

CAD relative polar entry

Typing @length<angle specifies a point at the given distance and angle from the previous point, using relative polar coordinates.

Boolean solid operations

Union merges solids, subtract removes one solid's volume from another, and intersect keeps only the shared volume of the selected solids.

Paper space viewport scale

In a layout, each viewport carries its own scale independent of model space geometry, and the plot style table maps object colours to pen widths.