**2.1 Traditional solutions**

The retention of a crown on a prepared tooth not only depends on the length and diameter of the walls of the preparation but also what is called the taper of the preparation. The angle formed between opposing walls of the tooth preparation for a crown is called taper or convergence angle (Rosenstiel, 1975). The retention of crowns decreases with increasing taper and has been shown to be inversely proportional to taper or convergence angle (Jorgenson, 1955). Therefore the higher the taper, the less retentive the crown and the more likely it will dislodge and come off the patient's tooth which is an undesirable outcome. The taper produced is in the hands of the dentist while the length and diameter of the walls are a function of the existing tooth. The ideal taper recommended is 4° - 14° total convergence angle (Shillingburg et al., 1997) and some dental schools also recommend similar angles (Noonan & Goldfogel, 1991; Robinson & Lee, 2001). Taper has been measured previously by various methodologies using replicas of the tooth preparations called dies and a microscope (Ohm & Silness, 1978), photocopying (Noonan & Goldfogel, 1991), use of shadowgraphs (Weed et al., 1984; Sato et al., 1998), overhead projectors (Nordlander et al., 1988; Patel et al., 2005) and a goniometer microscope (Ayad et al., 2005).

The replicas of the teeth or dies are made from dental stone and these dies represent the tooth that has been prepared in the patient's mouth. The three dimensional shape has four sides and one top or occlusal surface. Two walls that oppose each other are called mesial and distal and the other two are called buccal and lingual. It is the angle formed by two opposing walls, for example between the buccal and lingual walls (in the bucco-lingual plane) which is measured as Figure 1.

Fig. 1. Showing buccal and lingual walls (left) and mesial and distal walls (right)

Ohm and Silness (1978) projected the external contour lines of the preparation (of nearly 200 dies) and enlarged them onto the screen of the microscope and then measured the convergence angle. Noonan and Goldfogel (1991) used photocopy machines to copy over 900 dies. The dies were placed so that the shadow picture passed through the mesio-distal plane and then the images were produced on the copy paper. Lines were drawn on the surface planes of the shadow picture and the angle of convergence calculated.

Sato et al., (1998) investigated over 60 dies by projecting the silhouettes of the dies in a mesio-distal and bucco-lingual plane with a profile projector at magnification and traced them onto paper. Lines were drawn parallel to the walls and extended until they met and formed the convergence angle which was measured with a protractor. Patel et al., (2005) conducted investigations of convergence angle by also projecting silhouettes of 240

formed between opposing walls of the tooth preparation for a crown is called taper or convergence angle (Rosenstiel, 1975). The retention of crowns decreases with increasing taper and has been shown to be inversely proportional to taper or convergence angle (Jorgenson, 1955). Therefore the higher the taper, the less retentive the crown and the more likely it will dislodge and come off the patient's tooth which is an undesirable outcome. The taper produced is in the hands of the dentist while the length and diameter of the walls are a function of the existing tooth. The ideal taper recommended is 4° - 14° total convergence angle (Shillingburg et al., 1997) and some dental schools also recommend similar angles (Noonan & Goldfogel, 1991; Robinson & Lee, 2001). Taper has been measured previously by various methodologies using replicas of the tooth preparations called dies and a microscope (Ohm & Silness, 1978), photocopying (Noonan & Goldfogel, 1991), use of shadowgraphs (Weed et al., 1984; Sato et al., 1998), overhead projectors (Nordlander et al., 1988; Patel et al.,

The replicas of the teeth or dies are made from dental stone and these dies represent the tooth that has been prepared in the patient's mouth. The three dimensional shape has four sides and one top or occlusal surface. Two walls that oppose each other are called mesial and distal and the other two are called buccal and lingual. It is the angle formed by two opposing walls, for example between the buccal and lingual walls (in the bucco-lingual

Ohm and Silness (1978) projected the external contour lines of the preparation (of nearly 200 dies) and enlarged them onto the screen of the microscope and then measured the convergence angle. Noonan and Goldfogel (1991) used photocopy machines to copy over 900 dies. The dies were placed so that the shadow picture passed through the mesio-distal plane and then the images were produced on the copy paper. Lines were drawn on the

Sato et al., (1998) investigated over 60 dies by projecting the silhouettes of the dies in a mesio-distal and bucco-lingual plane with a profile projector at magnification and traced them onto paper. Lines were drawn parallel to the walls and extended until they met and formed the convergence angle which was measured with a protractor. Patel et al., (2005) conducted investigations of convergence angle by also projecting silhouettes of 240

Fig. 1. Showing buccal and lingual walls (left) and mesial and distal walls (right)

surface planes of the shadow picture and the angle of convergence calculated.

2005) and a goniometer microscope (Ayad et al., 2005).

plane) which is measured as Figure 1.

sectioned dies onto a flat surface by means of an overhead projector. This methodology was used previously by Nordlander et al., (1988). The devices such as photocopiers and overhead projectors were inexpensive to use and easily available. However the projecting of the dies to produce silhouettes would produce some error due to a 3-D object being measured as a 2-D image. Also, with the overhead projector there may have been inaccuracy due to the magnification of the image.

Ayad et al., (2005) used a goniometer microscope to measure the convergence angle of silhouettes of almost 500 die specimens in the mesio-distal and bucco-lingual plane. The angle formed with one prepared wall e.g. the buccal wall, and the vertical crosshair within the focusing screen was measured in degrees with the vernier scale on the microscope. The taper or convergence angle was calculated by adding the buccal and opposing lingual measurements. The goniometer microscope is a more expensive device than the ones used previously but more highly accurate.

Several studies conducted using these traditional methodologies investigating tapers achieved by dental students have found mean tapers ranging from 11° – 27° (Noonan & Goldfogel, 1991; Robinson & Lee, 2001; Smith et al., 1999; Mack, 1980; Ohm & Silness, 1978; Sato et al., 1998; Patel et al., 2005; Ayad et al., 2005) while studies on specialists and general dental practitioners and have found mean tapers in the range 14° - 20° (Patel et al., 2005; Nordlander et al., 1988; Kent et al., 1988; Eames et al., 1978). Even though higher than ideal tapers are found in some studies, tapers of up to 20° have been shown to be clinically acceptable with only a few crowns that were reported to have loosened and lost retention or dislodged(Ohm & Silness,1978; Sato et al., 1998).
