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Aims: Management of vertically fractured mandibular first molar by intra coronal splinting applying the finite centre of rotation effect of Pythagorus theorem. Case Presentations: A 28 year old male patient presented at the Department of Conservative Dentistry and Endodontics with the chief complaint of pain in the lower right back region of the mouth since last the 10 days. Past dental history revealed that affected tooth had root canal treatment done two years ago. History of present illness was that pain was elicited on chewing, and applying pressure on that area, with occasional bleeding from the same region. Intraoral examination revealed that tooth 46 was tender on percussion with vertically fractured crown in Case Study Tripathi et al.; BJMMR, 7(7): 623-629, 2015; Article no.BJMMR.2015.369 624 mesiodistal direction. Periapical Radiograph revealed that tooth was endodontically treated, with radiolucencies at apical and furcal area, and visible fracture line in mesiodistal direction at CEJ level. Technique Used in the Study: The tooth was endodontically retreated and Pythagorus theorem was used to locate the centres of rotation on both buccal and lingual sides of tooth 46 coronally. The technique was followed by drilling a vent at the same position approximating a fibre post (3M, Relyxfibre post). The centres were different both for buccal and lingual aspects which when approximated will provide antirotation. The post was placed in the buccolingual direction and the tooth was restored with posterior composites after which the restoration was checked for any high points. Follow up of the case was done for the period of one year. Discussion: The concept of the estimation of the finite centre of rotation is like the primary objective in tightening a screw joint to generate an optimum preload that will maximize the fatigue life of the screw while offering a reasonable degree of protection against loosening. The major advantage of this approach is that the fragment was stabilized properly and there was healthy development of periodontium over the year. Conclusion: Usually the vertically fractured tooth have poor prognosis and may likely be referred for extraction if not stabilized properly. This case report emphasizes the basic concept of stabilization and preventing rotation around an axis which will give the fractured tooth a better longevity and avoid the vibrations during crown preparation. The combined effect will restore the patient’s own natural tooth back and minimizes the chances of periodontal complication.

Bilateral inverted impacted third molar is a very rare incidence. Dearth of dental arch length and space are also considered as the chief cause for tooth impaction. Reviewing the literatures, mandibular third molar was the most frequently impacted tooth, followed by the maxillary third molars, the maxillary canines and the mandibular premolars.

The mandibular first molars ( primary and permanent) usually have 2 roots located mesially and distally, but occasionally they have an additional root located distolingually requiring special attention when root canal treatment is being considered . The additional root is regarded as a normal racial and morphological variation rather than as an abnormality. It appears to be more common in races of Mongoloid origin, including Malay, Chinese, Japanese, Eskimo, and American and Canadian Indian populations. 1 To study about the rarest root and root canal anatomy using spiral ct and r.v.g. Computed tomography and radio visiography has long been used as a diagnostic aid in dentistry .With the advent of new diagnostic aids like spiral computed tomography it has become very easy for the dentist to diagnose different root and root canal anatomy and accordingly plan the treatment.