Tangents

Alejandro Rivero, Sep 30, 2023

Collection of constructible tangents between parabola, circle and line

Table of Contents

  1. simple
    1. Parabola: tangent and normal at point
    2. Tangent to a circle across an external point
    3. Tangent to parabola across external point
    4. Three tangent circles
    5. Normals to Parabola across external point, Barton's
    6. Parabola: critical point for two extra normals
  2. advanced notes
    1. Parabola: tangent at a point
    2. tangents: Circle to circle and line
    3. X(181) Apollonius point
    4. Teorema de los círculos de Descartes (o Soddy)
    5. Satz von DESCARTES
  3. On constructibility
    1. Cuberoot by Descartes
    2. trisectie met parabool
  4. solving sextics
  5. Twitter hire problem
    1. Tangent problem from @iwontoffendyou
    2. Hire problem, initial setup
    3. Hire problem, False resolution
    4. Hire problem, Distance to parabola
    5. Hire problem, three locii

1.

simple

  • 1. Parabola: tangent and normal at point
  • 2. Tangent to a circle across an external point
  • 3. Tangent to parabola across external point
  • 4. Three tangent circles
  • 5. Normals to Parabola across external point, Barton's
  • 6. Parabola: critical point for two extra normals

1.1.

Parabola: tangent and normal at point

– Alejandro Rivero

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

2.

advanced notes

  • 1. Parabola: tangent at a point
  • 2. tangents: Circle to circle and line
  • 3. X(181) Apollonius point
  • 4. Teorema de los círculos de Descartes (o Soddy)
  • 5. Satz von DESCARTES

2.1.

Parabola: tangent at a point

– Alejandro Rivero

2.2.

–

2.3.

–

2.4.

–

2.5.

–

3.

On constructibility

See https://scholar.google.com/scholar?cites=17140011326199893149&as_sdt=2005&sciodt=0,5&hl=es https://scholar.google.com/scholar?cites=9170401149101633095&as_sdt=2005&sciodt=0,5&hl=es and equations in https://doi.org/10.1017/S0025557200176302 But note that the whole point is that the parabola itself is not a rule and compass construction. https://en.wikipedia.org/wiki/Straightedge_and_compass_construction

  • 1. Cuberoot by Descartes
  • 2. trisectie met parabool

3.1.

Cuberoot by Descartes

– Matthias Hornof

3.2.

–

4.

solving sextics

https://maa.org/press/periodicals/convergence/descartes-method-for-constructing-roots-of-polynomials-with-simple-curves-sextic-and-quintic


    This chapter does not contain any resources yet.

5.

Twitter hire problem

See https://twitter.com/CJHandmer/status/1705455384683598065/photo/1 and the twitter thread for solutions

  • 1. Tangent problem from @iwontoffendyou
  • 2. Hire problem, initial setup
  • 3. Hire problem, False resolution
  • 4. Hire problem, Distance to parabola
  • 5. Hire problem, three locii

5.1.

Tangent problem from @iwontoffendyou

– Alejandro Rivero

5.2.

–

5.3.

–

5.4.

–

5.5.

–

Information