text: Exercise on Ideal Desargues Figures
  28jun10
  
  \begin{document}
  \maketitle
  
  \section{Introduction}
  To appreciate what you learned in lesson P1 on Kepler's extended plane,
  it is instructive to continue the lesson, A9, on Desargue's Theorem,
  by drawing Desargue's figure when some of the given points are ideal.
  
  \subsection{KSEG experiments}
  You can use KSEG here is two ways. For the first, draw the standard
  Desargues figure, where all given points are in the finite plane. Then
  distort the picture, by pushing one points, for example $D$, further and
  further away from the other points. The three lines $(AA'), (BB'), (CC')$
  will approach being parallel. The second method is to "go to the limit".
  Thus $D$ is ideal means that the three lines are given to be parallel
  in the Euclidean plane. Show experimentally that Desargues' theorem still
  holds in this case, by choosing the points $A,A',B,B',C,C'$ on the three
  parallel lines, but then constructing the points $A^*=(BC)(B'C')$ etc, and
  showing that these three points, $(A^* B^* C^*)$  are  collinear.
  
  \section{Exercise: D is ideal}
  Submit a .seg file of Desargues' figure when $D=(AA')(BB')(CC')$ is ideal.
  
  \subsection{Hint}
  An outline of the solution was already given above.
  
  \section{Exercise: A is ideal}
  Submit a .seg file of Desargues' figure when $A$ is ideal
  
  \subsection{Hint}
  This one you need to think about carefully. For $A$ to be ideal,
  the two lines $(AC)$ and $(AB)$ have to be parallel in the Euclidean
  plane. What about the line $(AA')$ ? Since this line also passes through
  the same ideal point $A$ it must be parallel to the other two line through
  $A$.
  \end{document}
explanation: The document is a set of instructions and exercises related to Desargues' Theorem, specifically focusing on scenarios where some points are ideal (at infinity). It includes an introduction, a section on using KSEG for experiments, and two exercises with hints. The exercises require the submission of .seg files for specific configurations of Desargues' figure.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Exercise on Ideal Desargues Figures
  28jun10
  
  \begin{document}
  \maketitle
  
  \section{Introduction}
  To appreciate what you learned in lesson P1 on Kepler's extended plane,
  it is instructive to continue the lesson, A9, on Desargue's Theorem,
  by drawing Desargue's figure when some of the given points are ideal.
  
  \subsection{KSEG experiments}
  You can use KSEG here is two ways. For the first, draw the standard
  Desargues figure, where all given points are in the finite plane. Then
  distort the picture, by pushing one points, for example $D$, further and
  further away from the other points. The three lines $(AA'), (BB'), (CC')$
  will approach being parallel. The second method is to "go to the limit".
  Thus $D$ is ideal means that the three lines are given to be parallel
  in the Euclidean plane. Show experimentally that Desargues' theorem still
  holds in this case, by choosing the points $A,A',B,B',C,C'$ on the three
  parallel lines, but then constructing the points $A^*=(BC)(B'C')$ etc, and
  showing that these three points, $(A^* B^* C^*)$  are  collinear.
  
  \section{Exercise: D is ideal}
  Submit a .seg file of Desargues' figure when $D=(AA')(BB')(CC')$ is ideal.
  
  \subsection{Hint}
  An outline of the solution was already given above.
  
  \section{Exercise: A is ideal}
  Submit a .seg file of Desargues' figure when $A$ is ideal
  
  \subsection{Hint}
  This one you need to think about carefully. For $A$ to be ideal,
  the two lines $(AC)$ and $(AB)$ have to be parallel in the Euclidean
  plane. What about the line $(AA')$ ? Since this line also passes through
  the same ideal point $A$ it must be parallel to the other two line through
  $A$.
  \end{document}
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a set of instructions and exercises related to Desargues' Theorem, specifically focusing on scenarios where some points are ideal (at infinity). It includes an introduction, a section on using KSEG for experiments, and two exercises with hints. The exercises require the submission of .seg files for specific configurations of Desargues' figure.
  
  Label: multiple-question-and-answer