Geometry
http://www.maa.org/taxonomy/term/42302/0
enOn the Measure of Solid Angles
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-measure-of-solid-angles
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author revisits formulas of measuring solid angles that he could find only in centuries-old literature, and provides modern versions of the proofs.</em></p>
</div></div></div>Determinantal Loci
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/determinantal-loci
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>This article characterizes the points \((x, y)\) in the plane for which the determinant of a matrix of a particular form involving \((x, y)\) is \(0\). The matrices of interest have the form \(A+xL+uM\), where \(A\), \(L\), and \(M\) are square matrices, \(L\) and \(M\) are of rank one, and \(L + M\) is of rank two.</em></p>
</div></div></div>A Geometrical Approach to Cramer's Rule
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometrical-approach-to-cramers-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Motivated by the interpretation of a determinant of a \(2 \times 2\) matrix as the area of a parallelogram, the author derives Cramer's rule geometrically.</em></p>
</div></div></div>A Picture is Worth a Thousand Words
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-picture-is-worth-a-thousand-words
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author provides geometric illustrations of four subspaces associated with a matrix. Thinking of a matrix as a map between real vector spaces, the illustrations motivate the decomposition of the domain and range into orthogonal subspaces and the decomposition of vectors into orthogonal components. The author also indicates how the illustrations can be related to the solvability of certain matrix equations.</em></p>
</div></div></div>A Geometric Approach to Linear Functions
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-geometric-approach-to-linear-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>There are three somewhat distinct topics in this article: the condition for linear functions to commute, a linear function as a transformation of the number line, and linear difference equations. A linear function \(y=f(x)=ax+b\) can be characterized in terms of slope and the “center of reflection,” both of which reflect the geometric property of the function. </em></p>
</div></div></div>The Axis of a Rotation: Analysis, Algebra, Geometry
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-axis-of-a-rotation-analysis-algebra-geometry
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Given any 3 by 3 rotation matrix \(A\) (i.e. orthogonal with determinant \(1\) and an arbitrary vector \(x\), the vector \( Ax +A^{T}x+[1−\)tr\((A)]x\) lies on the axis of rotation. The article provides three different approaches, requiring various levels of background knowledge, to prove and/or explain the given result.</em></p>
</div></div></div>Proof without Words: A 2 x 2 Determinant Is the Area of a Parallelogram
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proof-without-words-a-2-x-2-determinant-is-the-area-of-a-parallelogram
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author presents a visual proof that the determinant of a 2 by 2 matrix equals the area of the corresponding parallelogram.</em></p>
</div></div></div>Finding the Volume of an Ellipsoid Using Cross-Sectional Slices
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/finding-the-volume-of-an-ellipsoid-using-cross-sectional-slices
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author shows that the volume of an ellipsoid can be determined by three parallel slices.</em></p>
</div></div></div>A Surprise from Geometry
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-surprise-from-geometry
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Consider \(n\) vectors issuing from the origin in \(n\)-dimensional space. The author shows that the statement “any set of \(n\) vectors in \(n\)-space, no two of which meet at greater than right angles, can be rotated into the non-negative orthant” is true for \(n \leq 4\), but false for \(n>4\).</p>
</div></div></div>An Infinite Series for \(\pi\) with Determinants
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/an-infinite-series-for-pi-with-determinants
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author gives an expression for \(\pi\) involving an infinite sequence of determinants, each representing the area of a triangle.</em></p>
</div></div></div>Definitely \(\sim\) Positively the Pits
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/definitely-sim-positively-the-pits
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author classifies the quadratic forms defined by simple 2 by 2 matrices and illustrates them with corresponding quadratic surfaces.</em></p>
</div></div></div>Linear transformation applet
http://www.maa.org/programs/faculty-and-departments/course-communities/linear-transformation-applet-0
Eigen demo with sound
http://www.maa.org/programs/faculty-and-departments/course-communities/eigen-demo-with-sound
Computer Graphics Project
http://www.maa.org/programs/faculty-and-departments/course-communities/computer-graphics-project
Geometry of Linear Transformations of the Plane
http://www.maa.org/programs/faculty-and-departments/course-communities/geometry-of-linear-transformations-of-the-plane