Canary Islands PAU Technical Drawing II flashcards

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

Circumcentre of a triangle

Intersection of the perpendicular bisectors of the three sides; equidistant from the vertices and the centre of the circumcircle. Inside an acute triangle, on the hypotenuse midpoint for a right triangle, outside for obtuse.

Euler line

The line through the circumcentre O, centroid G and orthocentre H of any non-equilateral triangle, with OG : GH = 1 : 2. It fixes the relative positions of these three notable points.

Regular polygon interior angle

For a regular n-gon each interior angle equals 180° − 360°/n, while the central angle between adjacent vertices measured from the centre is 360°/n. The sum of all interior angles is (n − 2)·180°.

Inradius formula

For a triangle, the inradius equals the area divided by the semiperimeter: r = A/s. The incentre is the intersection of the angle bisectors and is equidistant from all three sides.

Homothety ratio properties

A homothety of centre O and ratio k maps P to P′ on line OP with OP′ = k·OP. Lengths scale by |k|, areas by k², angles are preserved, and negative k places P′ on the opposite ray.

Composition of two reflections

Two reflections in parallel axes separated by d give a translation of 2d perpendicular to the axes. Two reflections in intersecting axes give a rotation about the intersection point through twice the angle between the axes.

Inversion definition

Given centre O and power r², the inverse P′ of P satisfies OP·OP′ = r² with O, P, P′ collinear. The transformation is conformal; lines not through O map to circles through O.

Similarity area and volume ratios

If two similar figures have corresponding lengths in ratio k, their areas are in ratio k² and their volumes in ratio k³. Corresponding angles are equal and orientation may be preserved or reversed.

Tangent from external point

Draw the circle with diameter OP where O is the given circle's centre and P the external point; its intersections with the given circle are the tangent points, because the radius there is perpendicular to the tangent.

Ellipse focal property

An ellipse is the locus of points whose distances to two fixed foci add to a constant 2a. With semi-minor axis b and focal distance c, a² = b² + c² and eccentricity e = c/a is less than one.

Parabola focus-directrix property

A parabola is the locus of points equidistant from a fixed focus and a fixed directrix. With vertex at the origin and axis along x, its equation is y² = 2px, where p is the focal parameter.

Hyperbola asymptotes

For a hyperbola with transverse semi-axis a and conjugate semi-axis b, the asymptotes are the lines y = ±(b/a)x through the centre. The relation c² = a² + b² gives eccentricity e = c/a greater than one.

Common tangents count

Two separate non-touching circles have four common tangents, two external and two internal. Externally tangent circles have three, overlapping circles two, internally tangent one, and one inside the other none.

True length right-triangle method

True length of a segment equals the hypotenuse of a right triangle whose legs are the projected length and the difference of the missing coordinates. It applies to lines oblique to the projection plane.

Line piercing a plane

Pass an auxiliary projecting plane through the line, intersect it with the given plane to obtain a line, and the point where that line meets the given line is the piercing point.

Line perpendicular to plane

A line is perpendicular to a plane when its projections are perpendicular to the corresponding traces, or to the principal lines of the plane. The plane then contains a line perpendicular to the given line.

Parallel planes condition

Two planes are parallel when two intersecting lines of one are respectively parallel to two intersecting lines of the other. Their traces of the same name are then parallel in both projections.

True shape of section

Obtain it by introducing a new projection plane parallel to the cutting plane, then projecting the section orthogonally onto it. Every segment of the section then appears at its true length.

Cone development sector angle

A right cone of base radius r and slant height g develops into a circular sector of radius g whose angle is 360°·r/g. The base circle is added separately to complete the development.

Euler polyhedron formula

For any convex polyhedron, vertices minus edges plus faces equals two: V − E + F = 2. It holds for the five regular solids, prisms, pyramids and all convex combinations.

Prism lateral development

Unfold the lateral surface as consecutive rectangles whose widths equal the true lengths of the base edges, taken from a true-shape view of the base. Add both bases at the appropriate edges.

First-angle view placement

In first-angle projection the object lies between observer and plane. The top view is placed below the front view and the left-side view on the right of the front view.

Third-angle view placement

In third-angle projection the plane lies between observer and object. The top view appears above the front view and the right-side view to its right, matching the truncated-cone symbol.

Auxiliary view purpose

An auxiliary view projects onto a plane perpendicular to one principal plane and inclined to another, showing the true shape of an inclined face or the true length of an oblique edge.

Scale calculation

Scale equals drawing length divided by real length. At 1:50 a real 2 m object measures 40 mm on paper; at 2:1 a 20 mm object measures 40 mm.

Isometric drawing axes

Isometric axes are drawn at 30° to the horizontal with equal full-size lengths along all three, giving an isometric drawing about 1.22 times the true isometric projection, which foreshortens by 0.816.

Cabinet oblique projection

The front face is drawn true shape in the picture plane, and receding edges are drawn at a chosen angle, usually 45°, at half scale. Cavalier uses full scale on the receding axis instead.

Isometric circle ellipse axes

A circle of diameter d on an isometric face becomes an ellipse whose major axis is perpendicular to the face normal and equals 1.22·d, with minor axis 0.71·d.

Four-centre ellipse method

Construct the isometric square as a rhombus, then draw arcs centred at the two obtuse corners and at points on the long diagonal. The four arcs join to approximate the isometric ellipse.

ISO A-series ratio

A0 has an area of one square metre with sides in ratio 1:√2, about 841 by 1189 mm. Each subsequent size halves the longer side, giving A4 as 210 by 297 mm.

Dimension figure placement

Dimension figures are placed above the dimension line, readable from the bottom or the right edge of the sheet. The unit is stated once in the title block and omitted from individual values.

ISO line type conventions

Continuous thick lines show visible outlines, continuous thin lines show dimensions and hatching, dashed lines show hidden outlines, and chain thin lines mark centre lines, axes and cutting planes.