# The Metrical Matrix in Teaching Mineralogy

G. V. Gibbs
,
Virginia Polytechnic Institute and State University
Author Profile

#### Summary

The calculation of the d-spacings, the angles between planes and zones, the bond lengths and angles and other important geometric relationships for a mineral can be a tedious task for the student and the instructor, particularly when completed with the large assortment of trigonometric identities and algebraic formulae that are available. However, such calculations are straightforward and relatively easy to do when completed with the metrical matrix and the interactive software MATOP. Several applications of the matrix are presented here, each of which is worked out in detail and which is designed to teach its use in the study of crystal geometry.

Used this activity? Share your experiences and modifications

## Context

#### Audience

This activity is designed for an undergraduate required course in mineralogy and is generally for sophomore or junior level students.

#### Skills and concepts that students must have mastered

Students should have an understanding of general mineralogy and crystal geometry. Students should also be familiar with solving mathematical matricies.

#### How the activity is situated in the course

This activity is a stand-alone exercise, but is part of a larger volume of classroom and laboratory activities from "Teaching Mineralogy," a workbook published by the Mineralogical Society of America, Brady, J., Mogk, D. W., and Perkins, D., (editors), 1997,406 pp.

## Goals

#### Content/concepts goals for this activity

This exercise is designed to aid in student understanding of crystal geometry, including d-space, bond length, bond angle, and other calculations.

## Description of the activity/assignment

The calculation of the d-spacings, the angles between planes and zones, the bond lengths and angles and other important geometric relationships for a mineral can be a tedious task for the student and the instructor, particularly when completed with the large assortment of trigonometric identities and algebraic formulae that are available. However, such calculations are straightforward and relatively easy to do when completed with the metrical matrix and the interactive software MATOP. Several applications of the matrix are presented here, each of which is worked out in detail and which is designed to teach its use in the study of crystal geometry.

## Supporting references/URLs

Brady, J., Mogk, D. W., and Perkins, D., (editors), 1997, Teaching Mineralogy, a workbook published by the Mineralogical Society of America, 406 pp.