diff --git a/extra/automata/automata.factor b/extra/automata/automata.factor
index b6d4152d0e..a70eaa063d 100644
--- a/extra/automata/automata.factor
+++ b/extra/automata/automata.factor
@@ -1,6 +1,6 @@
 
 USING: kernel math math.parser random arrays hashtables assocs sequences
-       vars ;
+       grouping vars ;
 
 IN: automata
 
@@ -32,29 +32,16 @@ dup >rule-number rule-values rule-keys [ rule> set-at ] 2each ;
 ! step-wrapped-line
 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
-: 3nth ( n seq -- slice ) >r dup 3 + r> <slice> ;
-
-! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-
-: map3-i ( seq -- i ) length 2 - ;
-
-: map3-quot ( seq quot -- quot ) >r [ 3nth ] curry r> compose ; inline
-
-: map3 ( seq quot -- seq ) >r dup map3-i swap r> map3-quot map ; inline
-
-! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
-
-: pattern>state ( {_a_b_c_} -- state ) rule> at ;
+: pattern>state ( {_a_b_c_} -- state ) >array rule> at ;
 
 : cap-line ( line -- 0-line-0 ) { 0 } prepend { 0 } append ;
 
 : wrap-line ( a-line-z -- za-line-za )
 dup peek 1array swap dup first 1array append append ;
 
-: step-line ( line -- new-line ) [ >array pattern>state ] map3 ;
-
-: step-capped-line ( line -- new-line ) cap-line step-line ;
+: step-line ( line -- new-line ) 3 <clumps> [ pattern>state ] map ;
 
+: step-capped-line  ( line -- new-line ) cap-line  step-line ;
 : step-wrapped-line ( line -- new-line ) wrap-line step-line ;
 
 ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
diff --git a/extra/automata/ui/ui.factor b/extra/automata/ui/ui.factor
index 467db53366..cfec6597c2 100644
--- a/extra/automata/ui/ui.factor
+++ b/extra/automata/ui/ui.factor
@@ -15,7 +15,7 @@ USING: kernel namespaces math quotations arrays hashtables sequences threads
        ui.gadgets.grids
        ui.gadgets.theme
        namespaces.lib assocs.lib vars
-       rewrite-closures automata ;
+       rewrite-closures automata math.geometry.rect ;
 
 IN: automata.ui
 
diff --git a/extra/color-picker/color-picker.factor b/extra/color-picker/color-picker.factor
index 99968ca3c3..6fcf3c21cd 100755
--- a/extra/color-picker/color-picker.factor
+++ b/extra/color-picker/color-picker.factor
@@ -3,7 +3,7 @@
 USING: kernel math math.functions math.parser models
 models.filter models.range models.compose sequences ui
 ui.gadgets ui.gadgets.frames ui.gadgets.labels ui.gadgets.packs
-ui.gadgets.sliders ui.render ;
+ui.gadgets.sliders ui.render math.geometry.rect ;
 IN: color-picker
 
 ! Simple example demonstrating the use of models.
diff --git a/extra/jamshred/jamshred.factor b/extra/jamshred/jamshred.factor
index b7764894d1..d9a0f84b53 100755
--- a/extra/jamshred/jamshred.factor
+++ b/extra/jamshred/jamshred.factor
@@ -1,6 +1,9 @@
 ! Copyright (C) 2007, 2008 Alex Chapman
 ! See http://factorcode.org/license.txt for BSD license.
-USING: accessors alarms arrays calendar jamshred.game jamshred.gl jamshred.player jamshred.log kernel math math.constants namespaces sequences threads ui ui.backend ui.gadgets ui.gadgets.worlds ui.gestures ui.render math.vectors ;
+USING: accessors alarms arrays calendar jamshred.game jamshred.gl
+jamshred.player jamshred.log kernel math math.constants namespaces
+sequences threads ui ui.backend ui.gadgets ui.gadgets.worlds
+ui.gestures ui.render math.vectors math.geometry.rect ;
 IN: jamshred
 
 TUPLE: jamshred-gadget jamshred last-hand-loc alarm ;
diff --git a/extra/math/geometry/rect/rect-tests.factor b/extra/math/geometry/rect/rect-tests.factor
new file mode 100644
index 0000000000..0d2a8bc1ea
--- /dev/null
+++ b/extra/math/geometry/rect/rect-tests.factor
@@ -0,0 +1,37 @@
+
+USING: tools.test math.geometry.rect ;
+
+IN: math.geometry.rect.tests
+
+[ T{ rect f { 10 10 } { 20 20 } } ]
+[
+    T{ rect f { 10 10 } { 50 50 } }
+    T{ rect f { -10 -10 } { 40 40 } }
+    rect-intersect
+] unit-test
+
+[ T{ rect f { 200 200 } { 0 0 } } ]
+[
+    T{ rect f { 100 100 } { 50 50 } }
+    T{ rect f { 200 200 } { 40 40 } }
+    rect-intersect
+] unit-test
+
+[ f ] [
+    T{ rect f { 100 100 } { 50 50 } }
+    T{ rect f { 200 200 } { 40 40 } }
+    intersects?
+] unit-test
+
+[ t ] [
+    T{ rect f { 100 100 } { 50 50 } }
+    T{ rect f { 120 120 } { 40 40 } }
+    intersects?
+] unit-test
+
+[ f ] [
+    T{ rect f { 1000 100 } { 50 50 } }
+    T{ rect f { 120 120 } { 40 40 } }
+    intersects?
+] unit-test
+
diff --git a/extra/maze/maze.factor b/extra/maze/maze.factor
index dbf983be62..389dabc0f6 100644
--- a/extra/maze/maze.factor
+++ b/extra/maze/maze.factor
@@ -1,7 +1,7 @@
 ! From http://www.ffconsultancy.com/ocaml/maze/index.html
 USING: sequences namespaces math math.vectors opengl opengl.gl
 arrays kernel random ui ui.gadgets ui.gadgets.canvas ui.render
-math.order ;
+math.order math.geometry.rect ;
 IN: maze
 
 : line-width 8 ;
diff --git a/extra/processing/processing.factor b/extra/processing/processing.factor
index fb9f321f47..4c9dd787e5 100755
--- a/extra/processing/processing.factor
+++ b/extra/processing/processing.factor
@@ -10,7 +10,7 @@ USING: kernel namespaces threads combinators sequences arrays
        combinators.cleave
        rewrite-closures fry accessors newfx
        processing.color
-       processing.gadget ;
+       processing.gadget math.geometry.rect ;
        
 IN: processing
 
diff --git a/extra/springies/springies.factor b/extra/springies/springies.factor
index 2640423eb4..fb69783975 100755
--- a/extra/springies/springies.factor
+++ b/extra/springies/springies.factor
@@ -38,6 +38,8 @@ C: <node> node
 
 ! : >>vel ( node vel -- node ) over set-node-vel ;
 
+: node-vel ( node -- vel ) vel>> ;
+
 : set-node-vel ( vel node -- ) swap >>vel drop ;
 
 : pos-x ( node -- x ) pos>> first ;
diff --git a/extra/tetris/tetris.factor b/extra/tetris/tetris.factor
index c2f874598c..d01cec3790 100644
--- a/extra/tetris/tetris.factor
+++ b/extra/tetris/tetris.factor
@@ -2,7 +2,8 @@
 ! See http://factorcode.org/license.txt for BSD license.
 USING: alarms arrays calendar kernel ui.gadgets ui.gadgets.labels
 ui.gadgets.worlds ui.gadgets.status-bar ui.gestures ui.render ui
-tetris.game tetris.gl sequences system math math.parser namespaces ;
+tetris.game tetris.gl sequences system math math.parser namespaces
+math.geometry.rect ;
 IN: tetris
 
 TUPLE: tetris-gadget tetris alarm ;
diff --git a/extra/ui/gadgets/borders/borders-tests.factor b/extra/ui/gadgets/borders/borders-tests.factor
index 268d1ab0a3..0151996c02 100644
--- a/extra/ui/gadgets/borders/borders-tests.factor
+++ b/extra/ui/gadgets/borders/borders-tests.factor
@@ -1,6 +1,6 @@
 IN: ui.gadgets.borders.tests
 USING: tools.test accessors namespaces kernel
-ui.gadgets ui.gadgets.borders ;
+ui.gadgets ui.gadgets.borders math.geometry.rect ;
 
 [ { 110 210 } ] [ <gadget> { 100 200 } >>dim 5 <border> pref-dim ] unit-test
 
diff --git a/extra/ui/gadgets/frame-buffer/frame-buffer.factor b/extra/ui/gadgets/frame-buffer/frame-buffer.factor
index a288f74f64..7d77db24cc 100644
--- a/extra/ui/gadgets/frame-buffer/frame-buffer.factor
+++ b/extra/ui/gadgets/frame-buffer/frame-buffer.factor
@@ -1,7 +1,7 @@
 
 USING: kernel alien.c-types combinators sequences splitting grouping
        opengl.gl ui.gadgets ui.render
-       math math.vectors accessors ;
+       math math.vectors accessors math.geometry.rect ;
 
 IN: ui.gadgets.frame-buffer
 
diff --git a/extra/ui/gadgets/gadgets-tests.factor b/extra/ui/gadgets/gadgets-tests.factor
index dbb2919277..1bea304f15 100755
--- a/extra/ui/gadgets/gadgets-tests.factor
+++ b/extra/ui/gadgets/gadgets-tests.factor
@@ -2,39 +2,7 @@ IN: ui.gadgets.tests
 USING: accessors ui.gadgets ui.gadgets.packs ui.gadgets.worlds
 tools.test namespaces models kernel dlists dequeues math sets
 math.parser ui sequences hashtables assocs io arrays prettyprint
-io.streams.string ;
-
-[ T{ rect f { 10 10 } { 20 20 } } ]
-[
-    T{ rect f { 10 10 } { 50 50 } }
-    T{ rect f { -10 -10 } { 40 40 } }
-    rect-intersect
-] unit-test
-
-[ T{ rect f { 200 200 } { 0 0 } } ]
-[
-    T{ rect f { 100 100 } { 50 50 } }
-    T{ rect f { 200 200 } { 40 40 } }
-    rect-intersect
-] unit-test
-
-[ f ] [
-    T{ rect f { 100 100 } { 50 50 } }
-    T{ rect f { 200 200 } { 40 40 } }
-    intersects?
-] unit-test
-
-[ t ] [
-    T{ rect f { 100 100 } { 50 50 } }
-    T{ rect f { 120 120 } { 40 40 } }
-    intersects?
-] unit-test
-
-[ f ] [
-    T{ rect f { 1000 100 } { 50 50 } }
-    T{ rect f { 120 120 } { 40 40 } }
-    intersects?
-] unit-test
+io.streams.string math.geometry.rect ;
 
 [ { 300 300 } ]
 [
diff --git a/extra/ui/gadgets/grids/grids-tests.factor b/extra/ui/gadgets/grids/grids-tests.factor
index f20275ff25..cfca5d5a93 100644
--- a/extra/ui/gadgets/grids/grids-tests.factor
+++ b/extra/ui/gadgets/grids/grids-tests.factor
@@ -1,5 +1,5 @@
 USING: ui.gadgets ui.gadgets.grids tools.test kernel arrays
-namespaces ;
+namespaces math.geometry.rect ;
 IN: ui.gadgets.grids.tests
 
 [ { 0 0 } ] [ { } <grid> pref-dim ] unit-test
diff --git a/extra/ui/gadgets/packs/packs-tests.factor b/extra/ui/gadgets/packs/packs-tests.factor
index 28a656e2ad..4ae84f83df 100644
--- a/extra/ui/gadgets/packs/packs-tests.factor
+++ b/extra/ui/gadgets/packs/packs-tests.factor
@@ -1,6 +1,6 @@
 IN: ui.gadgets.packs.tests
 USING: ui.gadgets.packs ui.gadgets.labels ui.gadgets ui.render
-kernel namespaces tools.test math.parser sequences ;
+kernel namespaces tools.test math.parser sequences math.geometry.rect ;
 
 [ t ] [
     { 0 0 } { 100 100 } <rect> clip set
diff --git a/extra/ui/gadgets/scrollers/scrollers-tests.factor b/extra/ui/gadgets/scrollers/scrollers-tests.factor
index 4df92141ba..cfbb1fdca5 100755
--- a/extra/ui/gadgets/scrollers/scrollers-tests.factor
+++ b/extra/ui/gadgets/scrollers/scrollers-tests.factor
@@ -3,7 +3,7 @@ USING: ui.gadgets ui.gadgets.scrollers namespaces tools.test
 kernel models models.compose models.range ui.gadgets.viewports
 ui.gadgets.labels ui.gadgets.grids ui.gadgets.frames
 ui.gadgets.sliders math math.vectors arrays sequences
-tools.test.ui ;
+tools.test.ui math.geometry.rect ;
 
 [ ] [
     <gadget> "g" set
diff --git a/extra/ui/gadgets/tracks/tracks-tests.factor b/extra/ui/gadgets/tracks/tracks-tests.factor
index e2db914089..d3264b2470 100644
--- a/extra/ui/gadgets/tracks/tracks-tests.factor
+++ b/extra/ui/gadgets/tracks/tracks-tests.factor
@@ -1,4 +1,4 @@
-USING: kernel ui.gadgets ui.gadgets.tracks tools.test ;
+USING: kernel ui.gadgets ui.gadgets.tracks tools.test math.geometry.rect ;
 IN: ui.gadgets.tracks.tests
 
 [ { 100 100 } ] [