Phillips Exeter Math Examples

Emma, Jun 23, 2015

Table of Contents

  1. Math 230
    1. Parabola Construction
    2. dihedral
  2. Math 310
    1. Volume of a Sphere
  3. Math 320
    1. Matrix Transformations
  4. Math 340
    1. Candle Slice
    2. Sliced Tetrahedron
  5. Math 430
    1. Math 4 72/2
    2. Math 4 73/1
    3. Math 4 74/7
  6. Math 510
    1. Three dimensional parametric path
    2. Osculating Plane as Intersection of Normal Planes

1.

Math 230

  • 1. Parabola Construction
  • 2. dihedral

1.1.

Parabola Construction

Drag N and observe the location of P, the intersection of the perpendicular bisector of FN and the line through N perpendicular to AB. Turn the Trace of P on to keep track of P's location, or look at the locus of P to see its complete path. [br][br]What happens to your graph if you move F or the line AB?[br][br]Note: when you turn off Trace, click and drag a point in the background to erase your old trace.
Emma Phillips[br]March 2016[br]Phillips Exeter Academy
– Emma

1.2.

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2.

Math 310

  • 1. Volume of a Sphere

2.1.

Volume of a Sphere

Emma Phillips[br]March 2016[br]Phillips Exeter Academy
– Emma

3.

Math 320

  • 1. Matrix Transformations

3.1.

Matrix Transformations

Plug in matrices to explore the transformations they create when applied to the unit square. Try creating a reflection, a rotation, a dilation, and any combinations of the above. Are there any points that are fixed, regardless of the matrix?
Matrix Transformations
Emma Phillips[br]Phillips Exeter Academy[br]June 2015
– Emma

4.

Math 340

  • 1. Candle Slice
  • 2. Sliced Tetrahedron

4.1.

Candle Slice

A cylindrical candle of diameter 2 with a piece of paper wrapped around it is sliced at a [math]45^{\circ}[/math] angle. Assume the cut is made 3 units from the base of the candle. When the paper is unrolled, what does the cut edge of the paper look like?

Emma Phillips Phillips Exeter Academy July 2015
– Emma

4.2.

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5.

Math 430

  • 1. Math 4 72/2
  • 2. Math 4 73/1
  • 3. Math 4 74/7

5.1.

Math 4 72/2

Use the slider for 'a' to see the triangular cross sections of Sasha's figure.
Emma Phillips[br]Phillips Exeter Academy[br]February 2016
– Emma

5.2.

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5.3.

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6.

Math 510

  • 1. Three dimensional parametric path
  • 2. Osculating Plane as Intersection of Normal Planes

6.1.

Three dimensional parametric path

On the left you will see the path (2cost, 2sint, sin(3t)). Use slider k to move a particle along the path and see its velocity vector. On the right, you can see the speed of the particle (marked by B).

This is from Math 510 at Phillips Exeter Academy; it is problem 9/7. Emma Phillips Phillips Exeter Academy October 2015
– Emma

6.2.

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