Skip to content

EV1 interactive #1033

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
siwelwerd wants to merge 5 commits into
base: main
Choose a base branch
from
+84 −26
Open

EV1 interactive #1033

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
5 commits
Select commit Hold shift + click to select a range
5ea9afa
EV1 interactive
siwelwerd May 12, 2026
16aa3f8
Fix errors
siwelwerd May 12, 2026
b8bc3d3
Swap out map for repeat
siwelwerd May 13, 2026
928753c
Update interactive
siwelwerd May 13, 2026
f6873f3
Tweaks
siwelwerd May 13, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
12 changes: 6 additions & 6 deletions source/linear-algebra/source/01-LE/01.ptx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -508,15 +508,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s

<figure xml:id="figure-intersecting-planes-one">
<caption>Intersection of three planes at one point</caption>
<image xml:id="LE1-image-intersection-planes-one" width="50%" component="print">
<image xml:id="LE1-image-intersection-planes-one-print" width="50%" component="print">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-one.sage" parse="text"/>
</sageplot>
<description>
<p>Three planes are shown to intersect at a single point. An arrow points to the point of intersection at coordinates <m>(1,2,3)</m>.</p>
</description>
</image>
<image xml:id="LE1-image-intersection-planes-one" component="html">
<image xml:id="LE1-image-intersection-planes-one-html" component="html">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-one.sage" parse="text"/>
</sageplot>
Expand All @@ -528,15 +528,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s

<figure xml:id="figure-intersecting-planes-inf">
<caption>Intersection of three planes at a line</caption>
<image xml:id="LE1-image-intersection-planes-inf" width="50%" component="print">
<image xml:id="LE1-image-intersection-planes-inf-print" width="50%" component="print">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-inf.sage" parse="text"/>
</sageplot>
<description>
<p>Three planes are shown to intersect along a line of points.</p>
</description>
</image>
<image xml:id="LE1-image-intersection-planes-inf" component="html">
<image xml:id="LE1-image-intersection-planes-inf-html" component="html">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-inf.sage" parse="text"/>
</sageplot>
Expand All @@ -548,15 +548,15 @@ system). Otherwise it is <term>inconsistent</term>.<idx><h>inconsistent linear s

<figure xml:id="figure-intersecting-planes-zero">
<caption>Three non-mutually-intersecting planes</caption>
<image xml:id="LE1-image-intersection-planes-zero" width="50%" component="print">
<image xml:id="LE1-image-intersection-planes-zero-print" width="50%" component="print">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-zero.sage" parse="text"/>
</sageplot>
<description>
<p>Three planes are shown to intersect at no common point, although each pair of planes intersects along a line of points.</p>
</description>
</image>
<image xml:id="LE1-image-intersection-planes-zero" component="html">
<image xml:id="LE1-image-intersection-planes-zero-html" component="html">
<sageplot variant="3d" aspect="1.0">
<xi:include href="./sage/LE1-image-intersection-planes-zero.sage" parse="text"/>
</sageplot>
Expand Down
39 changes: 19 additions & 20 deletions source/linear-algebra/source/02-EV/01.ptx
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -221,27 +221,26 @@ we refer to this real number as a <term>scalar</term>.
</p>
</task>
<task>
<p component="html">
Correct the SageMath code cell below to generate
an illustration of several vectors belonging to
<me>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right],
\left[\begin{array}{c}-1\\1\end{array}\right]\right\}=
\setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+
b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR}</me>
in the <m>xy</m> plane.
</p>
<sage component="html">
<input>
<xi:include href="./code/ev1-planar-span.sage" parse="text" />
</input>
</sage>
<p component="html">
Based on this illustration, which of these geometrical objects
best describes the span of these two vectors?
<p>
In addition to the combinations above, use the interactive below to graph an additional
5 or more vectors belonging to
<me>\vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right],
\left[\begin{array}{c}-1\\1\end{array}\right]\right\}=
\setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+
b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR}</me>
in the <m>xy</m> plane.
</p>
<p component="print">
Which of these geometrical objects
best describes the span of these two vectors?
<interactive label="EV1-interactive-span" platform="doenetml" width="100%">
<slate surface="doenetml">
<xi:include parse="text" href="doenet/EV1-span-two-vectors.xml"/>
</slate>
<description>
<p>An interactive that graphs linear combinations of the vectors <m>\left[\begin{array}{c}1\\2\end{array}\right]</m> and
<m> \left[\begin{array}{c}-1\\1\end{array}\right]</m>.</p>
</description>
</interactive>
<p>
Which of these geometrical objects best describes the span of these two vectors?
</p>
<ol marker="A." cols="4">
<li>A line</li>
Expand Down
59 changes: 59 additions & 0 deletions source/linear-algebra/source/02-EV/doenet/EV1-span-two-vectors.xml
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,59 @@
<p>
Enter several pairs of coefficients <m>(a,b)</m>, separated by commas:
<mathInput name="in" minwidth="500" prefill="(1,1),(-2,1),(-1,-2)" />
</p>

<setup>
<math name="v"> (1,2)</math>
<math name="w"> (-1,1)</math>
<mathList name="l">$in</mathList>
<sampleRandomNumbers numSamples="10" from="-6" to="6" name="a" asList="true"/>
<sampleRandomNumbers numSamples="10" from="-6" to="6" name="b" asList="true"/>
</setup>

<triggerSet>
<!--<callAction actionName="deleteChildren" target="$g" number="1000"/>-->
<callAction actionName="addChildren" target="$g">
<vector draggable="false" styleNumber="1" head="$v" />
<label anchor="$v" positionFromAnchor="right">
<m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
</label>
<vector draggable="false" styleNumber="2" head="$w" />
<label anchor="$w" positionFromAnchor="left">
<m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
</label>
<repeat for="$l" valueName="c">
<vector draggable="false" styleNumber="3" head="$c.x*$v+$c.y*$w"/>
</repeat>
</callAction>

<label>Plot the above linear combinations</label>
</triggerSet>

<callAction actionName="deleteChildren" target="$g" number="1000"><label>Reset plot</label></callAction>

<triggerSet>
<label>Add 10 random linear combinations</label>

<callAction target="$a" actionName="resample"/>
<callAction target="$b" actionName="resample"/>
<callAction actionName="addChildren" target="$g">
<repeatForSequence from="0" to="10" step="1" valueName="i">
<vector draggable="false" styleNumber="4" head="$a[$i]*$v+$b[$i]*$w"/>
</repeatForSequence>
</callAction>
</triggerSet>

<graph name="g" xmin="-10" ymin="-10" xmax="10" ymax="10">
<description>Graph of two vectors and linear combinations thereof</description>

<vector draggable="false" styleNumber="1" head="$v" />
<label anchor="$v" positionFromAnchor="right">
<m>\left[\begin{array}{c} $v.x \\ $v.y\end{array}\right]</m>
</label>
<vector draggable="false" styleNumber="2" head="$w" />
<label anchor="$w" positionFromAnchor="left">
<m>\left[\begin{array}{c} $w.x \\ $w.y\end{array}\right]</m>
</label>

</graph>
Loading