Kaufmannmathway

AuthorIndexAAbánades,M.
,230,238Adams,M.
,15,85Adams,W.
W.
,316Aho,A.
V.
,122Aldon,G.
,309Aleven,V.
,361Allen,S.
F.
,73Alsina,C.
,141,146Anderson,J.
R.
,291,294,354,355Antonini,S.
,174,187,188,190Appel,K.
,139,154Armand,M.
,74,80,83Arora,S.
,125Arsac,G.
,118,183Artaud,M.
,128Artigue,M.
,165,288Arzarello,F.
,157,176,178,183,332,336,342Asher,N.
,21Asperti,A.
,15,73,85Assaf,A.
,354Attridge,N.
,290Avigad,J.
,15,73,85,278Awtry,T.
,314BBaccaglini-Frank,A.
,174,184,185,188,190,359Bachmair,L.
,74Back,R.
J.
,328Baeta,N.
,250Bainville,E.
,256Baker,S.
,65Balacheff,N.
,128,142,158,173,233,331,337,358,360Ballantyne,A.
M.
,21Bancerek,G.
,73,352Barak,B.
,125Barany,M.
,205Barbin,.
,141Barbosa,H.
,75Baron,G.
L.
,117Barra,M.
,149Barrett,C.
,74,77Bartle,R.
G.
,158BartoliniBussi,M.
G.
,147,175,177,178,332,358Barwise,J.
,289Barzilay,R.
,19Basu,S.
,116Bauer,G.
,15,85Baulac,Y.
,219Beeson,M.
,22,314,326,327Bellemain,F.
,219Bérard,B.
,127Berger,M.
,255Bernardo,G.
,314,320Bertot,Y.
,15,85Besson,F.
,73,78,79Bezem,M.
,238,245Bieda,K.
N.
,173Biere,A.
,74Bikner-Ahsbahs,A.
,332,342Bjrner,N.
,74,75Blanchette,J.
C.
,74Blazy,S.
,86Bledsoe,W.
W.
,21Blok,W.
J.
,96SpringerNatureSwitzerlandAG2019G.
Hannaetal.
(eds.
),ProofTechnologyinMathematicsResearchandTeaching,MathematicsEducationintheDigitalEra14,https://doi.
org/10.
1007/978-3-030-28483-1367Blum,W.
,147Boaler,J.
,204,205,207Boero,P.
,173,177,182,183,358,359Boesen,J.
,313,322Boespug,M.
,81Bhme,S.
B.
,74Bolyard,J.
J.
,332Bonacina,M.
P.
,86Bonnycastle,J.
F.
,320Boole,G.
,314Borromeo-Ferri,R.
,147Borwein,J.
M.
,116,256Bosbach,B.
,96Botana,F.
,218,219,230,238,240,250Bouallegue,S.
,250Bouhineau,D.
,313,326Boulmé,S.
,86Bourdieu,P.
,201–203Boutin,F.
,143Bouton,T.
,74,78Boyer,R.
S.
,21,22Boyle,C.
F.
,291,354Brach,C.
,335Brancker,T.
,328Brousseau,G.
,128,140,156,158,164Bruillard,.
,117Brummayer,B.
,74Bryant,J.
,147Buchberger,B.
,20,220,221,223Büchi,J.
R.
,96Bueno-Ravel,L.
,117Bundy,A.
,14,66,70,209,327Burel,G.
,354Burkhardt,H.
,327Burris,S.
,91Byliński,C.
,73,352CCaferra,R.
,361Calegari,F.
,203Campos,H.
,250Carmen,B.
,314,320Carter,N.
C.
,290Castelnuovo,E.
,149Cauderlier,R.
,354Chaachoua,H.
,313,326Chabert,J.
L.
,116Chazan,D.
,335Chen,C.
,358Cheng,Y.
-H.
,294Chernoff,E.
J.
,337Chevallard,Y.
,157Chou,S.
C.
,215,218,219,238–242,245–247,249Clairaut,A.
C.
,140–142,148,154Clarke,D.
,343Clarke,E.
,22Cobb,P.
,240,356,361Coen,C.
S.
,73Cohen,C.
,15,85Coles,A.
,343Colliard,M.
N.
,121Colton,S.
,116Constable,R.
L.
,19,73Conway,C.
L.
,74Coquand,T.
,245Corbeil,J.
P.
,154–156Corbett,A.
T.
,294,355Corless,R.
M.
,220Cormack,L.
B.
,147Cormen,T.
H.
,125Cornilleau,P.
-E.
,78,79Corpuz,J.
,217,218Coutat,S.
,147,158Crǎciun,A.
,20Cramer,M.
,22Crowdmath,207Cruz-Filipe,L.
,76DDaCosta,N.
C.
A.
,119Dahn,B.
I.
,91Dale,R.
,27Dang,D.
T.
,15,85Dapueto,C.
,359Davis,P.
J.
,205,231Dawkins,P.
C.
,358Deaney,R.
,239deBruijn,N.
G.
,60Déharbe,D.
,74,78Delahaye,D.
,354Delignat-Lavaud,A.
,74,86deMorgan,A.
,199deMoura,L.
M.
,73–75,77Dénès,M.
,81deOliveira,D.
,74,78Derouet,C.
,145,156Deters,M.
,74deVilliers,M.
,110,173,191,219,232,233,237,239,256,291,331,358Dimova,D.
,74D'Mello,S.
,337Douady,R.
,130Dowek,G.
,354368AuthorIndexDoyle,W.
,294Dreyfus,T.
,165,176Dubois,C.
,354Duponsel,N.
,332–334,336,337,342–344Dupré,S.
,139,148,149Durand-Guerrier,V.
,118,121Durell,C.
V.
,320duSautoy,M.
,200,203,209Duval,R.
,140,141,158,173,176,357,358Dweck,C.
S.
,204EEaton,R.
,73Ebner,G.
,354Edelson,D.
,294Efremovitch,V.
A.
,269Ehrhardt,C.
,202Ekici,B.
,74,81,85Elia,I.
,144Engle,R.
A.
,343Etchemendy,J.
,289Euler,L.
,314Evan,R.
,314,320FFaure,G.
,74,80,83Felty,A.
,19,20Ferrari,P.
,359Ferreirim,I.
M.
A.
,96Ferrero,E.
,359Ferri,F.
,177Fietzke,A.
,74Fillitre,J.
-C.
,74,86Fischbein,E.
,186Flajolet,P.
,125Fontaine,P.
,74,78Font,L.
,140,163Forest,S.
,74,86Fortuny,J.
M.
,140,240,361Foster,C.
,221Fournet,C.
,86Frege,G.
,119Fugard,A.
,66Fugard,A.
J.
B.
,68Fujita,T.
,173,291,292,296,298,300,308Fuller,E.
,308Fu,Z.
,74GGagatsis,A.
,145Gagnon,M.
,140,154–156,163Galperin,G.
A.
,255Ganesalingam,M.
,21,24Ganzinger,H.
,74Gao,X.
S.
,238–242,245–247,249García-Diez,M.
,142Gardner,M.
,261Garillot,F.
,15,85Garuti,R.
,173,177,182,183,358,359Geeraerts,L.
,149Gelernter,H.
,218,355,360Gentry,C.
,86Gerdes,A.
,326Giorgiutti,I.
,141Gdel,K.
,59,65Godot,K.
,121Goldstein,I.
,354Gonthier,G.
,15,85González,G.
,291Gordon,M.
,73Gowers,T.
,202,205,206Grabowski,A.
,73,352Graesser,A.
,337Graham-Lengrand,S.
,86Gravemeijer,K.
,336Gravier,S.
,121,150,153Gray,E.
,150Greeno,J.
G.
,298Grégoire,B.
,73,74,80,81,83Grenier,D.
,117,121Gribomont,P.
,118,119,125,126Grice,H.
P.
,29Grover,B.
W.
,295Gueudet,G.
,117Gutiérrez,.
,256,335HHadarean,L.
,74Hadas,N.
,176,178Hhnle,R.
,353Haken,W.
,139,154Hales,T.
C.
,15,85Halmos,P.
R.
,220Hanna,G.
,173,176,204,231,232,237,238,256,291,357Hardy,G.
H.
,199,200,206,207,209,210Harel,G.
,173,183,256Harris,M.
,200,203,204Harrison,J.
,15,73,85,357Hart,E.
W.
,117Haek,R.
,230Haspekian,M.
,156Hauer,B.
,359,360Healy,L.
,332,335,359Heeren,B.
,326Heidigger,M.
,208AuthorIndex369Heinze,A.
,294Henneman,W.
H.
,21Hennessy,S.
,239Henningsen,M.
,295Herbelin,H.
,73Herbst,P.
G.
,173,291,335,358Hershkowitz,R.
,178,337Hersh,R.
,205Hetzl,S.
,354Heule,M.
J.
H.
,74,75,85,350Hilbert,D.
,60Hoang,T.
L.
,15Hoare,C.
A.
R.
,125Hodges,R.
,21Hoelzl,R.
,359Hoffmann,D.
L.
,142Hohenwarter,M.
,216,218,219,221,232,238,240,250Holland-Minkley,A.
M.
,19Hollings,C.
,199Hlzl,R.
,183Hopcroft,J.
,122,124,126Houdebine,J.
,141Howell,J.
,86Howson,A.
G.
,116,117,231Hoyles,C.
,239,331,335,359Hritcu,C.
,74,86Hsieh,F.
J.
,237Huet,G.
P.
,73Hughes,E.
K.
,343Humayoun,M.
,22Hurd,J.
,74IIl'jashenko,J.
S.
,269Inglis,M.
,290Ingold,T.
,198,208,209Iwanaga,Y.
,296JJackiw,N.
R.
,219Jahnke,H.
N.
,173Jamnik,M.
,65,66Janii,P.
,218,219,238–242,245–247,250Jaworski,B.
,220,221Jebelean,T.
,20Jenkins,A.
,201,202,210Jeuring,J.
,326Jiang,J.
,239Johnson,H.
L.
,343Jones,K.
,173,239,291,292,295,296,298,308,309,311,332,334,338,342–344,358Jones,P.
L.
,220Jourdan,J.
-H.
,86Jovanovic,D.
,74KKahane,J.
P.
,116,117Kaliszyk,C.
,74Kapur,D.
,218,240Katz,G.
,74,81,85Kaufmann,M.
,74Keller,A.
G.
,148Keller,C.
,74,80,81,83,85,86Keller,O.
,142King,T.
,74Kirshner,D.
,314Knipping,C.
,173Knott,A.
,28,29Knuth,E.
J.
,331Kcher,N.
,313,314,318–320Koedinger,K.
R.
,294,354,355Koepke,P.
,22Kohlhase,M.
,86Kohlweiss,M.
,86Koike,N.
,332Komatsu,K.
,291,332,334,335,338,342–344Konev,B.
,74–76Kong,S.
,73,278Korniowicz,A.
,73,352Kortenkamp,U.
,219,233,238,358,359Kovács,L.
,20Kovács,Z.
,163,216,218–222,224,228,230,232,233,238,240,250,359,360Ko,Y.
Y.
,331Krause,E.
F.
,228Kreitz,C.
,73Krieger,M.
H.
,152,157Küchemann,D.
,331Kuhlwein,D.
,22Kullmann,O.
,74,75,85,350Kumar,R.
,74Kutsia,T.
,20Kutzler,B.
,218Kuzniak,A.
,140,144,145,157LLaborde,C.
,141,147,158,179,332Laborde,J.
M.
,178,179,219,256,359Lagrange,J.
B.
,145Lakatos,I.
,5,60–62,64,69,207,292,331Lane,L.
,201,202,205Laporte,V.
,86Larsen,S.
,331370AuthorIndexLascarides,A.
,21Laval,D.
,145,157Lawrie,C.
,256Leduc,N.
,154–156,361Lehman,B.
,337LeHoang,T.
,85Leibniz,G.
,314Leiserson,C.
E.
,125Lei,D.
,147Leitsch,A.
,354Lemut,E.
,173,182,183,358,359Leron,U.
,186Leroy,X.
,86Lescuyer,S.
,74Leung,A.
Y.
L.
,174,178,183,186,188,190,332,358Levenson,E.
,314,320Levi-Strauss,C.
,208Lewis,R.
Y.
,278Li,H.
,240Lin,F.
L.
,237,294Lisitsa,A.
,74–76Lithner,J.
,313,322Lopez-Real,F.
,183,186Lorigo,L.
,73Loustaunau,P.
,316Lovász,L.
,117Luengo,V.
,292,297,308,359–361ukasiewicz,J.
,99Lund,T.
,320Lynce,I.
,74MMackenzie,D.
,73,205,208Mahboubi,A.
,73Malik,S.
,74Mancosu,P.
,15Manizade,A.
G.
,332Mannila,L.
,328Mante,M.
,183Maréchal,A.
,86Marek,V.
W.
,74,75,85,350Margolinas,C.
,158Marhajan,Y.
,74Mari,M.
,250Mariotti,M.
A.
,173–175,177,178,180,181,183–185,187,188,190,332,359Marradez,R.
,335Martinovic,D.
,332Martin,T.
S.
,157,291Martin,U.
,198,199,207Maschietto,M.
,147MasonJ.
,204Matsuda,N.
,356,361Matuszewski,R.
,73,352Mawer,R.
F.
,46Maxwell,E.
A.
,317McCrone,S.
S.
,291McCune,W.
,91MeavillaSeguí,V.
,240Meavilla,V.
,140,158,159,161Mebsout,A.
,74,81,85Mejia-Ramos,J.
P.
,308Meyer,A.
,125Michael-Chrysanthou,P.
,140Miller,D.
,19,20,86Milton,J.
A.
,142Miyazaki,M.
,173,291,292,296,298,300,308Modeste,S.
,117,125,128,150,153,154Moggi,E.
,102Monks,K.
G.
,290Moore,J.
S.
,22,74Morris,C.
W.
,119Morselli,F.
,173Motwani,R.
,122,124,126Moutet,L.
,145,157Moyer-Packenham,P.
S.
,332Murray-Rust,D.
,209NNakagawa,K.
,20Narboux,J.
,238,240,242,246,247Naumowicz,A.
,73,352Neale,V.
,206,209,210Nelsen,R.
B.
,65,66,141,146,239Netz,W.
,148Nevins,A.
J.
,354Newell,A.
,355Newman,M.
H.
A.
,320Nicaud,J.
F.
,313,326Nieuwenhuis,R.
,75Noel,W.
,148Norell,U.
,73Northrop,E.
P.
,317,320Noss,R.
,359OOhtani,M.
,295,343Oliveras,A.
,73Olivero,F.
,183,336Oller,A.
M.
,140,158,159,161OllerMarcén,A.
M.
,240Osana,H.
P.
,332–334,336,337,342–344Ouvrier-Buffet,C.
,117,150,153Owen,E.
,46AuthorIndex371Owens,K.
,358Owens,T.
M.
,96Owre,S.
,73PPalm,T.
,313,322Paneque,J.
,240Panero,M.
,00Paola,D.
,183,336Parisse,B.
,219Parno,B.
,86Paskevich,A.
,22,74,86Paulson,L.
C.
,74,23Pavlovi,V.
,238,242,245Payan,C.
,117,121Pedemonte,B.
,183,358Pegg,J.
,256Pekrun,R.
,337Peled,I.
,331Pelletier,R.
,294,355Pell,J.
,328Peltier,N.
,361Pepin,B.
,295,309,343Perrin,D.
,116Pesty,S.
,360Petrovi,I.
,218,219,238,240,250Pettitt,P.
B.
,142Pichardie,D.
,78,79,86Pike,W.
G.
,142Pollack,R.
,116Polya,G.
,164,165,205,313,326,358Polymath,D.
H.
J.
,198,205–207,209,210Potari,D.
,165Prank,R.
,326Prediger,S.
,165,332,342Presmeg,N.
C.
,335Protzenko,J.
,86Prusak,N.
,337Puertas,E.
,361Puitg,F.
,361Pulte,H.
,173Pye,D.
,208QQuaresma,P.
,238–242,246,247,250Quine,W.
V.
,119,120RRabardel,P.
,146,147,160Rabe,F.
,86Raffalli,C.
,22Rahn,J.
H.
,328Ramsden,P.
,322,323Ranise,S.
,77Rastogi,A.
,74,86Raykova,M.
,86Recio,T.
,140,145,154,163,216,218,219,221,230,232,238,240,250,359,360Reid,D.
A.
,173Reiser,B.
J.
,294Reis,G.
,354Reiss,K.
,294Reiter,E.
,27Reynolds,A.
J.
,74,81,85Reynolds,J.
C.
,128Rhoads,K.
,308Riazanov,A.
,74Ribbens,D.
,118,119,125,126Ricciotti,W.
,73Rice,A.
,199Richard,P.
R.
,140,144–147,154–156,158,163,230,240,361Richter-Gebert,J.
R.
,238,359Rivest,R.
L.
,125Roberts,S.
,200,202,203Robinson,A.
,60,197Robutti,O.
,174,183,336Roy,M.
F.
,116Rushby,J.
M.
,73Ruthven,K.
,165,239Ryle,G.
,200,206,208–210SSaillard,R.
,86,354Sakamaki,A.
,332Samkoff,A.
,308Sangwin,C.
J.
,147,313–315,317–323Santos,V.
,250Scali,E.
,359Schifer,K.
,228Schneider-Kamp,P.
,76Schoenfeld,A.
H.
,178,294Schrder,B.
,22Schulz,S.
,74Schumann,H.
,256,268,270Schwarz,B.
B.
,178,337Sedgewick,R.
,125Selden,A.
,182Selden,J.
,182Semadeni,Z.
,333Semliakov,A.
N.
,255Sethi,R.
,122Sewell,W.
H.
,201Shankar,N.
,73,86Shaw,355Sherbert,D.
R.
,158Sherin,B.
,294Shoeneld,J.
R.
,64372AuthorIndexSidoli,N.
,238Sieg,W.
,289Sierpinska,A.
,177Silva,J.
P.
M.
,74Simon,H.
,355Simon,M.
A.
,183Sinaceur,H.
,116,121Sinclair,N.
,174,358Smith,M.
S.
,343Sólyom-Gecse,C.
,230,238Soury-Lavergne,S.
,361Sowder,L.
,173,183Standish,C.
D.
,142Stefferud,E.
,355Stein,C.
,125Stein,M.
K.
,295,343Stevenson,I.
,178,332Stojanovi,S.
,238,242,245Strsser,R.
,178Straubing,H.
,126Stump,A.
,77,78Stylianides,A.
J.
,173,179,332,343Stylianides,G.
J.
,179,332,343Suda,M.
,74Sullivan,M.
C.
,141Su,Z.
,239,291,359Swamy,N.
,74,86Sweller,J.
,46TTabachnikov,S.
,255Takeuti,G.
,353Tall,D.
,150Tanguay,D.
,144,145,149,157Tanswell,F.
,204,208Tao,T.
,203–205,207,210Tarski,A.
,99,119–121Tassi,E.
,73Tessier-Baillargeon,M.
,154–156Théry,L.
,74,78,80,83TheTheoremaWorkingGroup.
,230Thomas,R.
,202,210Thomas,W.
,126,127Thompson,D.
R.
,190Tinelli,C.
,73,74,77,81,85Tirosh,D.
,314,320Tomaevi,J.
,242Toi,D.
,242Trahan,A.
,152,153,162,167Trilling,L.
,361Trouche,L.
,117,146Trybulec,A.
,22Tseitin,G.
,79Tsujiyama,Y.
,332Turnow,E.
,198UUfer,S.
,294Ullman,J.
D.
,122,124,126Urban,J.
,74,357VVajda,R.
,230Valcarce,J.
L.
,219vanDoorn,F.
,73,278vanMaaren,H.
,74Van,K.
,356,361Vélez,M.
P.
,140,154,163,221,230,238Vélez,P.
,359,360Velleman,D.
,289Venant,F.
,152,157Vergnaud,G.
,128Vershinin,K.
,22Villani,C.
,200Villiers,M.
,141Vitrac,B.
,148Vivier,L.
,145vonRaumer,J.
,73,278Voronkov,A.
,60,74Vujoevi-Janii,M.
,242WWallin,S.
,328Walsh,T.
,74Wang,D.
,240Wang,K.
,239,291,359Ward,M.
R.
,46Watson,A.
,295,343Weber,K.
,292,293,307,308,332,358,360Weber,T.
,74Weidenbach,C.
,74Weil,P.
,126Weiss,M.
,358Weller,D.
,354Werner,B.
,74,80,83Wiedijk,F.
,357Wiles,A.
,197,202,209,210Wilson,B.
,231Winker,S.
,91Winter,H.
,256Wischnewski,P.
,74Wittgenstein,L.
,119,120Wolper,P.
,118,119,125,126Wu,W.
,239,240AuthorIndex373YYackel,E.
,356Yerushalmy,M.
,335Ye,Z.
,238,240–242,246,249Yost,G.
,291,354ZZach,R.
,59,60Zahradník,J.
,230Zandieh,M.
,331Zaslavsky,O.
,331Zazkis,R.
,337Zeitz,P.
,205Zhang,J.
Z.
,238–240,245–247Zhao,X.
,22Zilho,J.
,142374AuthorIndexSubjectIndexAABC-conjecture,203Advancedgeometrytutor,361AgentGeom,361AlgebraicGeometry,215,218,228Algorithmic,117–119,123–125,127–129,131–134,136,150–157,161,162,164,166,167,232Algorithms,6,59,73,74,76,86,115–118,122–125,127–135,140,143,145,150–154,157,161,164,215,220,221,224,231,232,242,297Analogy,200,202,256,258,259,358Analysis,24,54,66,70,91,94,122,125,128,129,132–136,145,159,175,176,178,179,184,185,191,200,217,218,256,279,295,301,302,306,308,309,318,319,322,327,338,344,354Android/iOSmathappsEdukera,218Euclidea,218mathway,218photomath,218Angleproject,354Antiprismn-gonalantiprism,256Argumentation,8,176,183,190,322,323,328,356–359Articialmathematician,362ATP/automatedtheoremproving/automatedprovers,14,60,65,74,75,85,86,238,242,349–362Automata,122,124,126,127,131Automateddeductionautomateddeductioningeometry,218,219Automatedproofsearch,91Automaticdiscovery,217,231Automaticproving/automatictheoremprovergeometryautomatedtheoremprover,237–239,250Automationincombinatorics,75,85BBaghera,361BilliardsElementarybilliards,257Binaryoperation,20,92,96,284Bricolage,208CCabri3D,256,257Cabri-Euclide,297,359,361CabriGeometry/Cabri-géomètre,219,359Casediscrimination,256Catalansolids,271Causality,160,185,256Charisma,203,204Cinderella,219,238,359Complexity,27,124,125,129,130,132,133,136,154,157,162,177,191,192,200,239,240,349,357,358,360Composition,36,51,122,125,126,208,256,286Computeralgebra,215,219,224,350ComputeralgebrasystemGiac,219Computerscience,3,5,6,60,76,85,86,115–119,121,122,124–126,128,130,132,135,136,154,278,281,282,287,289,290SpringerNatureSwitzerlandAG2019G.
Hannaetal.
(eds.
),ProofTechnologyinMathematicsResearchandTeaching,MathematicsEducationintheDigitalEra14,https://doi.
org/10.
1007/978-3-030-28483-1375Concept,6,21,70,102,120,125,128–130,132,139–141,144,145,157,159,163,165,203,206–208,219,220,239,280,284,287,331,333–336,351,352,359Conception,119,128–131,133–135,145,158,284,357,360Conditionality,182,183,185Conjecture,3,5,7,15,62,65,68,74–77,85,86,91,92,94–98,100,101,103,107,116,142,154,162,167,173,182–185,187,191,199,203,206,207,216,217,220–223,226,237–241,243,245,249,250,256,331,333,335,336,350,351,358,359Construction,6,14,26,50,55,56,127,136,143,147,149,174,175,178–186,188–192,201,202,209,215,216,223,224,237–243,246,249,250,256,259,260,265,271,279,280,292,294,297,309,334,336–338,355,356,359,360,362Continuationmonad,102Constructiveomegarule,64–66,69Contradictions,55,59,79,93–95,131,156,185,186,279,289,314,320,333,334,337,340Convexhull,256,264,268,269,272Correctness,14,15,22,60,61,66,69,74,76,80,84–86,123–126,129,132,133,179,180,278,308,315–317,320,323,324,351,360Counterexample,5,8,95,101,121,207,223,239,331,333,335–340,342,343,359,361Craft,6,197,198,202,205,208,210Cube,61,63,64,169,256,257,259,260,262,264,265,267Cuboid,256,262Cutrule,353D3Ddynamicgeometrysystems,255–2573DhexagonEquiangular3Dhexagon,260Equilateral3Dhexagon,261,267Pointsymmetric3Dhexagon,266,269Regular3Dhexagon,267,268Self-intersecting3Dhexagon,268Symmetric3Dhexagon,2703Dkite,2713Dparallelogram,2713Dpolygon,61,2713Dquadrangle,257,270,2713Drhomb,270DeBruijncriterion,351,352Decompilationofcompiledcode,16Deduction,19,26,33,38–40,45,46,49,55,65,78,121,122,125,126,158,241,250,251,279,280,282–284,290,297,351,354Deltoid,269Diagram,36,66,68,69,145,146,148,149,157,159,162,216,222,297,332,334,335,337–339,342,343,354,355,360,361Diagrammaticreasoning,141Didacticheuristic,360Didactical/didactics,6,115,116,118,125,127,128,135,136,144,163,166DoublepyramidThree-sideddoublepyramid,268,269Draggingtest,179,180,336Dynamicgeometry,4,7,9,116,146,147,149,155,157,160,162,163,166,174,175,183,215–219,231,232,237,240,250,256,291,327,332,349,358DynamicGeometryEnvironment(DGE)/DynamicGeometrySystems(DGS),174,176,178–192,216,237,239,241,250,332–334,336–340,342,344,359–361EEffectiveness,118,154,190Elementarygeometryapolloniuscircle,227geometricmeantheorem,181,230Pythagoras'theorem,230righttrianglealtitudetheorem,230Thales'circletheorem,228triangleinequality,228,257Empiricalvalidation,356,358,361Enrichment,165Epistemicvalue,148,176,357Epistemologicalrevolution,356Epistemology,115,117Ethnography,204Explanation,7,15,75,80,110,188,217,237,238,241,250,256,305,336,357,362FFeedback,8,86,233,281,287,291,295–299,303,304,308,314,315,323,324,352,354,355,359,360376SubjectIndexFieldofexperience,359Formalism,59,60,126,132,278,354,357Formalization,5,15,59,152,154,357GGeneralization,36,152,166–168,228,230,256,262,265GeneralProblemSolver,355Genius,6,197,202–205,210GeoGebraAutomatedReasoningTools(ART),221,224,231,233envelopecommand,230LocusEquationcommand,217,222,225–229Relationcommand,216,223,224,226,227Provecommand,230,240ProveDetailscommand,230Geometer'sSketchpad,219,291GeometerSupposer,219Geometricreasoningalgorithm,217conjecture,216theorem,217Geometrygeometrical,178–181geometricconstruction,175,218,237,239,240,242,243,246geometriclocus,162,222,227spatialgeometry,255,256Geometrymachine,355Geometrytutor,354,355,361GooglePlay,218HHeuristicHeuristicargumentation,358,359Hexahedron,265,268–270Heytingalgebra,96,100–102,110Hilbert'sprogram,59,60,63,64,66,69,70Hoop,91,96–103,107,110Human-orientedhuman-likeoutput,22,25,29,31human-likewrite-ups,24human-orientedtheoremproving,21IImplicitlocus,221,222,228Indirectproof,174,185–187,190–192,292Induction,65,68,69,74,100,129,131,154,256,280,287,313,327,351,356,358InformationandCommunicationTechnology(ICT),6,173,174Interactivetheoremprover,5,14,15,73,278,281,284,288JJohnsonsolids,271Justication,18,27,45,78,93,94,133,244,313,320,323KKite,268,269,271LLanguage,7,19,20,27,59,115,118,120–124,126,127,131,132,134,141,165,190,205,237,238,240–242,245,246,248,250,277–282,284,286,288,289,297,314,352,354–357Lean,8,278–289,362Learningdiscoverylearning,7,9,143,154,205,218,220,221,237Learningandteachingofgeometrycomputer-mediatedthinking,218,220creativityspiral,217,220,226geometrycalculator,231–233mentor,204,217,221teachingtriad,220technology-mediatedparadigm,217Logic,7,8,23,30,60,73,75,85,86,91,92,96,99,100,115,116,118,119,121,122,125–128,131,136,145,149,155,156,163,176,179,218,242,245,277–284,286,288–290,327,350–353,355,362Logicalframework,127,352,354Logictheorist,355MMace4,5,91,92,95–98,100,101,110Manipulatives,8,332–337,342–344Mathematicalconcept,157,280,333,334Mathematicalpractice,116,198,204,205,208,331,333Mathematicalvirtues,204Mathematicalworkingspace,140,144,157,162,361Mathematics,3–6,8,9,15,23,27,59–61,68,76,85,100,115–118,121–123,128,130,131,134–136,140,143,144,SubjectIndex377147–149,153,154,156–159,163–166,173,176,177,181,191,197–200,202–205,207,208,210,215,217,220,228,231,233,237,238,256,278,280,282,284–292,294,295,300,301,313,314,318–320,323,327,328,331,332,336,343,349–352,356,357,359–362Meshwork,209Metaphorsofspaceandlandscape,198Methodheuristicmethod,163,265Metricspace,13,25,30,32,47Microworld,359,361Mindset,204,205,207Model,21,24,26,27,34,41,43,75,77,79,85,91,95,103,110,120–123,125–129,131–134,141–148,151–153,156–160,162,163,173,186,188,207,237,239,277,281,317,319,327,354,355,358,359,361Modelling,25,26,126,139,143,145,147,151,157,158,163,164Model-theoretic,110,119–121,127NNaturallanguage,7,19,21,27,29,123,141,165,240,242,245,246,250,281,354,357Networkingtheoreticalapproaches,342,3442n-gonRegular2n-gon,255Spatial2n-gon,256Non-example,335OOnticvalue,357Orbit,267Ordinalsum,99,100PPACTGeometryTutor,361Parallelogram,146,167,184,187,188,190,243,260,270,333–336,338,340,341Pedagogicalsupport,231,233,333,336,342,343Perimeterminimalperimeter,7,256,268,270Platonicsolids,61,271Pocrim,98,99Polygonconvexpolygon,168,255hexagonalpolygon,257inscribedpolygon,256Petriepolygon,256pointsymmetricpolygon,262,268–270spatialpolygon,269Polyhedraconvexpolyhedra,7,255,271Polyhedron2n-facedpolyhedron,255,256Polymath,6,198,205–207,209,210Pragmatics,40,119,123,136,154,280,355,361Programming,83,117,118,122,123,132–135,143,150,154,220,221,226,278Proofproofcerticate,308proofswithanaturallanguagerendering,7,242proofswithavisualrendering,7,246prooftheory,353,354prooftutor,289,354,356,359rigorousproof,5,60,63,152,157,224schematicproof,60,63–70,352Properties,158,160,163,167,180,184,185,190,237–241,243,250,257,258,280,286,300,302,305,307,308,315,316,324,327,350,357,359Prover9,5,91–97,100–104,107,110QQED-Tutrix,140,155,156,163,164,361Quadrilateral,64,184,187,188,190,300,333–336,338–341RReasoningreasoningbackwards,40,42,46reasoningforwards,24,28,35,38,40,46,47reasoningtactics,42,43,45–47Reection,27,135,148,173,201,204,246,256,257,259,260,264Refutation,3,245,291,332,334,343Reinforcement,204,238,240,256,284,335,357Representations,37,128,129,131–136,139–141,145–147,149,159,160,162–164,188,203,210,242,282,284,297,316,332–335,354–358,360Restructuring,256,355378SubjectIndexReversibility,256,265,321Rhombus,339Robbinsconjecture,91SSemantics,99,118,119,122,123,125,132,135,136,158,176,250,279,289,351,359Semilattice,91,92,94–97Semioticpotential,174–176,178–183,185,190,191Sequentcalculus,353Skill,4,6,66,136,173,198,202,204,205,207–210,221,290,350,355Socialmachine,198,206,209SpaceEuclideanspace,255virtualspace,257Specication,135,256,278,287,318Square,122,157,168,187,188,233,257–261,284,339Structuralinduction,126Students'perceptions,333,337Symmetry,24,104,116,203,266,268,269,353Syntax,8,83,92–94,119,120,122,123,126,135,136,222,281,284,288,289,322,352,360Synthesis,174,256TTask-basedinterview,332,333,337,338,342,343Taskdesign,8,294,295,301,309,332–337,342–344TechnologyEnhancedLearning(TEL),355–359,361Termination,124Tetrahedra,270TheoremCognitiveunityoftheorem,358modeloftheorem,361Theoremproving/proversautomatictheoremproving/provers,4,5,7,8,15,16,231,350interactivetheoremproving/provers,8,14,15,33,73,279–281,284Theoryofsemioticmediation,6,174,175Trajectory,255,257,258,260,263,264,267Trapezohedron,268Trapezoid,269Turingtest,362TwinPrimesconjecture,206VVariation,29,159,166,184,228,256Verication,3,7–9,15,24,60,66,86,110,118,127,129,132–134,139,152–154,160,168,176,217,221,232,237,238,240,242,256,278,289,322,352,353,356,361Vertices,61,126,131,184,189,221,222,247,256,262,263,268–270,333,336Virtualmanipulative,8,332,333,335–337,342,343WWayfarer,198,209SubjectIndex379