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<html>
<head><title>MATH 471</title>
<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-MML-AM_CHTML'></script>
</head>
<body bgcolor="#666666" link="#cccccc" text="#ccddcc">
<p>
<b> MATH 471, GEOMETRY FOR TEACHERS <br>
(Problem solving oriented introduction <br>
to Euclidean and non-Euclidean geometries.)</b>
</p>
<p>
<a href="sil.html"> Syllabus</a>
<!--
-
<a href="extra.pdf"> Extra credit problems</a>
-->
</p>
<hr color="#ccddcc" />
<ul>
<!--
<li> HWA-14, due 10:10, Mon, Dec 6.
<ul>
<li> Read: Chapters 14 and 15.</li>
<li> Exercises: 14.4, 14.9, 15.6, 15.9.</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Three%20pairs%20of%20parallel%20lines.html"> Three pairs of parallel lines (related to 15.8),</a></li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Third%20parallel%20line.html"> Third parallel line (related to 15.15),</a></li>
<li>Extra credit: <a href="https://anton-petrunin.github.io/birkhoff/car/Intersection point.html"> Intersection point.</a>
</li>
</ul>
</li>
</ul>
</li>
<li> HWA-13, due 10:10, Mon, Nov 29.
<ul>
<li> Read Chapter 19.</li>
<li> Play <A href="https://www.euclidea.xyz">Euclidea</A>.</li>
<li> Exercises: 19.7(a), 19.10, 19.14(a,b).</li>
<li> Constructions:
<ul>
<li> <A href="http://anton-petrunin.github.io/birkhoff/car/Pentagon.html"> Pentagon (19.7b)</li>
<li><A href="https://www.euclidea.xyz/en/game/10.8"> Chord trisection</li>
<li> <A href="http://anton-petrunin.github.io/birkhoff/car/Arithmetic construction.html"> Arithmetic construction</A></li>
<li> <A href="http://anton-petrunin.github.io/birkhoff/car/Square root.html"> Square root</A></li>
</ul>
</li>
</ul>
</li>
<li> HWA-12, due 10:10, Mon, Nov 15.
<ul>
<li> Skim thru chapters 11--13.</li>
<li> Start to read Chapter 19.</li>
<li> Exercises: 11.2, 12.2, 13.9.</li>
<li> Constructions:
<ul>
<li> <A href="https://www.euclidea.xyz/en/game/5.4"> Line equidistant from two points</A></li>
<li> <A href="https://www.euclidea.xyz/en/game/5.5"> Equal cuts</A></li>
<li> <A href="https://www.euclidea.xyz/en/game/6.4"> Angle with given bisector</A></li>
<li> <A href="https://www.euclidea.xyz/en/game/9.6"> Trisection by trapezoid diagonals</A></li>
</ul>
</li>
</ul>
</li>
</ul>
<hr color="#ccddcc" />
<ul>
<li> Мidterm: Fri, Nov 12, in class, 5 problems:
<ul>
<li> 2 theorems from the list (possibly with related definitions):<br>
10.15, 10.26,
11.1, 11.4, 11.8, 11.9,
12.6, 12.8, 12.10, 12.23,
13.2, 13.8, 13.10, <del>13.13</del>;
</li>
<li> 2 problems from HWA 08--11; </li>
<li> one new problem.</li>
</ul>
</li>
<li> You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
</li>
</ul>
<hr color="#ccddcc" />
<ul>
<li> HWA-11, due 10:10, Mon, Nov 8.
<ul>
<li> Read and understand: Chapter 13.</li>
<li> Exercises: 13.3, 13.6, 13.12, 13.14.</li>
<li> Constructions:
<ul>
<li> <A href="https://anton-petrunin.github.io/birkhoff/car/Bolyai construction.html"> Bolyai construction</A></li>
<li> <A href="https://anton-petrunin.github.io/birkhoff/car/Common h-perpendicular.html"> Common h-perpendicular</A></li>
</ul>
</li>
<li> Start to think about the second midterm --- skim thru chapters 11--13, prepare at least one question. </li>
</ul>
</li>
<li> HWA-10, due 10:10, Mon, Nov 1.
<ul>
<li> Read and understand: Chapter 12.
</li>
<li> Read and think: Chapter 13.
</li>
<li> Exercises: 12.1, 12.21, 12.24(d), 13.1.
</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/H-perpendicular.html"> h-perpendicular;</a>
</li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Tangent%20h-line.html"> Tangent h-line.</a>
</li>
</ul>
</li>
</ul>
</li>
<li> HWA-09, due 10:10, Mon, Oct 25.
<ul>
<li> Read and understand: Chapter 11.</li>
<li> Read and think: Chapter 12.</li>
<li> Exercises: 11.3, 11.10, 11.11, 11.13.</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/H-center.html"> h-center;</a></li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Equal%20h-radii.html"> Equal h-radiuses.</a>
</li>
</ul>
</ul>
</li>
<li> HWA-08, due 10:10, Mon, Oct 18.
<ul>
<li> Skim thru chapters 2--10.</li>
<li> Exercises: 7.26, 8.4, 9.4, 10.20.</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Apollonian%20circle.html"> Apollonian circle (7.27).</a>
</li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Equal%20angles.html"> Equal angles (9.20);</a></li>
</ul>
</ul>
</li>
</ul>
<hr color="#ccddcc" />
<p>
<ul>
<li> Midterm, Fri Oct 15, in class, 5 problems:
<ul>
<li> 2 theorems from the list (possibly with related definitions): <br>
2.5, 2.8, 2.13,
3.6, 3.12,
4.1, 4.2, 4.4,
5.2, 5.5, 5.10, 5.15, 5.17,
6.4,
7.1, 7.2, 7.8, 7.9, 7.18,
8.1, 8.3, 8.5, 8.8, 8.11,
9.1, 9.2, 9.13,
10.2, 10.6, 10.15, 10.25.
</li>
<li> 2 problems from HWA 01--07 </li>
<li> one new problem</li>
</ul>
</li>
<li> You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
</li>
<li>The office hours shifted to Thu, Oct 14, 17:00--17:50 <a href="https://psu.zoom.us/my/anton.petrunin"> psu.zoom.us/my/anton.petrunin</a> (this week only).</li>
</ul>
<hr color="#ccddcc" />
<ul>
<li> HWA-07, due 10:10, Mon, Oct 11.
<ul>
<li> Read and understand: Chapters 10.</li>
<li> Exercises: 10.4, 10.8, 10.13, 10.21.</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Perpendicular%20with%20ruler.html"> Perpendicular with ruler (9.11);</a></li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Perpendicular%20circles.html"> Perpendicular circles (10.22).</a>
</li>
</ul>
<li> Start to think about midterm exam --- skim thru the covered material, prepare at least one question. </li>
</ul>
</li>
<li> HWA-06, due 10:10, Mon, Oct 4.
<ul>
<li> Read Chapters 9 and 10.</li>
<li> Exercises: 8.16, 9.6, 9.17, 10.3.</li>
<li> Constructions:
<ul>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Right%20angles.html"> Right angles (9.9);</a>
</li>
<li><a href="https://anton-petrunin.github.io/birkhoff/car/Inversion.html"> Inversion (10.5).</a></li>
</ul>
<li> Extra exercise: 9.7 (Do it only if you have time; it will not be graded).</li>
</ul>
</li>
<li> HWA-05, due 10:10, Mon, Sep 27.
<ul>
<li> Read Chapter 7 and 8.</li>
<li> Read and think: Chapter 9.</li>
<li> Exercises: 7.10, 7.16, 7.24, 8.6.</li>
<li> Constructions:
<ul>
<li>
<a href="http://anton-petrunin.github.io/birkhoff/car/Segment trisection.html"> Segment trisection (7.11).</a>
</li>
<li>
<a href="https://anton-petrunin.github.io/birkhoff/car/Incircle.html"> Incircle.</a>
</li>
</ul>
</li>
</ul>
</li>
<li> HWA-04, due 10:10, Mon, Sep 20.
<ul>
<li> Read Chapter 6.
</li>
<li> Read and think: Chapter 7.
</li>
<li> Exercises: 4.7, 5.4, 5.20, 6.5.
</li>
<li> Constructions:
<ul>
<li>
<a href="http://anton-petrunin.github.io/birkhoff/car/Tangents to the circle.html"> Tangents to the circle (5.24);</a>
</li>
<li>
<a href="http://anton-petrunin.github.io/birkhoff/car/Parallel line.html"> Parallel line (7.5).</a>
</li>
</ul>
</li>
</ul>
</li>
<li> HWA-03, due 10:10, Mon, Sep 13.
<ul>
<li> Read and understand: Chapters 4 and 5.</li>
<li> Read and think: Chapter 6.</li>
<li> Exercises: 3.13, 4.3, 4.8, 5.3. (Scan to PDF and upload to CANVAS.)</li>
<li> Constructions (once you see "Well done", make a screenshot and upload it to CANVAS):
<ul>
<li>
<a href="http://anton-petrunin.github.io/birkhoff/car/Perpendicular.html"> Perpendicular (5.22)</a> (or <a href="https://www.euclidea.xyz/en/game/2.6"> 2.6 in Euclidea</a>);
</li>
<li>
<a href="http://anton-petrunin.github.io/birkhoff/car/Center of the circle.html"> Center of the circle (5.23)</a> (or <a href="https://www.euclidea.xyz/en/game/1.6"> 1.6 in Euclidea</a>).
</li>
</ul>
</li>
</ul>
</li>
-->
<li> HWA-02, due 15:35, Mon, Jan 27.
<ul>
<li> Skim thru Chapter 3; make sure that your intuition agrees with 3.7, 3.9, 3.10, 3.12, and 3.17.</li>
<li> Read Chapter 4.</li>
<li> Exercises: 3.13, 4.3, 4.6, 4.7, 4.8. (Scan to PDF and upload to CANVAS.)</li>
</ul>
</li>
<li> HWA-01, due 15:35, Fri, Jan 17.
<ul>
<li> Read the 2nd chapter (using the 1st chapter as a reference).</li>
<li> Exercises: 1.4, 1.5, 1.13, 2.12, 2.14; scan to PDF and upload to CANVAS.</li>
<li> <a href="https://www.geogebra.org/m/mv3z6jed#material/nfzrzg6d">Test construction</a> --- get to "Well done", make a screenshot, and upload it to CANVAS. This part will not be graded; it is to ensure that you can run these applets on your computer. (Spend no more than 3 minutes on it.)</li>
</ul>
</li>
</ul>
<hr color="#ccddcc" />
</body></html>