GC World : Various Problems

学年,ページ教科書対応コンテンツサブコンテンツ
年, p.4p4p The Concept of "Quadrangle→Quadrangle"
年, p.4p4p Connecting the midpoints of four sides : Exploring correspondence, : In the condition of particular shape, : In the condition of particular shape, : In the condition of particular shape,
年, p.4p4p Bisectors of four corners : Exploring correspondence, : In the condition of particular shape, : Always parallelogram,
年, p.4p4p Perpendicular bisectors of four sides : Exploring correspondence, : In the condition of particular shape, : Always parallelogram, : The result is one point, : The result is one point/Sets of corresponding points,
年, p.4p4p Perpendiculars from four corners to diagonals : In the case of rectangle, : In the case of parallelogram, : In the case of square, : In the case of general quadrangle,
年, p.center The Concept of "Five centroids of triangle etc."
年, p.center Circumcenter : Definition, : In the case of two lines, : To observe movement of circumcenter, : To observe movement of three lines, : To find place which satisfy a condition (1), : To find place which satisfy a condition (2), : To find place which satisfy a condition (3), : Special case (1), : Special case (2), : Realistic problems (1), : Realistic problems (2), : Realistic problems (2), : Realistic problems (4), : Realistic problems (5), : Three circles (1), : Three circles (2-1), : Three circles (2-2), : Three circles (3),
年, p.center Incenter : Definition, : In the case of two lines (1), : In the case of two lines (2), : In the case of two lines (3), : In the case of two lines (4),
年, p.center Barycenter : Definition, : To find the point which satisfy a condition,
年, p.center Orthocenter : Definition,
年, p.center Excenter : Definition,
年, p.center Fermat point : Definition, : To find the point which satisfy a condition, : How to draw,
年, p.complex The concept of "Complex Number"
年, p.complex Forming by {zn} : Exploring change, : Forming particular case,
年, p.complex Solution of quadratic equation : There is no real number solution, : Where is the complex number solution?, : Moving on an unit circle,
年, p.constant The concept of "Constant"
年, p.constant Area of triangle : Confirming with measurement, : In the case of other triangle, : Areas of two triangles,
年, p.constant Length of segment : Confirming with measurement, : Two segments, : Many segments,
年, p.constant Angle of corner : To equate two triangles, : To equate many angles, : Confirming (1), : Confirming (2),
年, p.constant Sum of segments : Measurement, : Many examples,
年, p.constant Sum of segments : Measurement and conjecture, : Measurement and conjecture, : Change the condition,
年, p.constant Sum of segments : Measurement and conjecture, : Measurement and conjecture, : Change the condition,
年, p.envelope The Concept of "Curves formed by lines"
年, p.envelope From perpendicular bisector : Horizontal, : Circle (1), : Circle (2),
年, p.func The concept of "Graph of Function"
年, p.func Linear Function : Plotting points (1), : Plotting points (2), : Plotting points (3), : Change of graph (1), : Change of graph (2), : Change of graph (3), : Change of graph (4), : Rate of change (1), : Rate of change (2), : Passing by two points, : Slope and one point (1), : Slope and one point (2), : Slope and one point (3), : Linear function passing by two points,
年, p.func Function proportional to square : Plotting (1), : Plotting (2), : Plotting (3), : Plotting (4), : Plotting (5), : Plotting (6),
年, p.func Quadratic function : Plotting (1), : Plotting (2), : Plotting (3),
年, p.func Trigonometric function : Drawing values (sin x), : Drawing values (cos x), : Drawing values (tan x), : Plotting (sin x), : Plotting (cos x), : Plotting (tan x),
年, p.func Visualisation of minimum value : Only one figure, : Measurement, : Calculating sum, : Drawing a graph,
年, p.locus2 The concept of "Sets of satisfied points"
年, p.locus2 ＰＡ＝ＰＢ : , : ,
年, p.locus2 ＰＡ＝２ＰＢ : , : ,
年, p.locus2 ＰＡ＝ＰＢ＋２ : , : ,
年, p.locus2 ＰＡ＋ＰＢ＝１０ : , : ,
年, p.max_min The concept of "Max・Min"
年, p.max_min Distance between two points : Confirming with measurement, : Confirming with additional line,
年, p.max_min Length of segment turned by straight line : Confirming with measurement, : Confirming with additional line, : Confirming with additional line,
年, p.max_min Length of segment turned by straight line : Confirming with measurement, : Confirming with additional line,
年, p.max_min Length of arc : Confirming with measurement, : Confirming with additional line,
年, p.max_min Area of triangle which inscribes in a circle : Confirming with measurement, : Decoding the meaning of additional line, : Decoding the meaning of additional line, : Measurement and conjecture,
年, p.max_min Perimeter of triangle which inscribes in a circle : Confirming with measurement, : Decoding the meaning of additional line, : Decoding the meaning of additional line, : Measurement and conjecture,
年, p.max_min Area of a triangle of which three points are each foot of perpendicular : Confirming with measurement (Maximum), : Confirming with measurement (Maximum), : Confirming with measurement (Minimum),
年, p.real Wiper : General wiper, : Wiper of bus, : Rear wiper,
年, p.real Swing : Swing (1), : Swing (2),
年, p.real Trisection machine of corner : Trisection machine of corner?,
年, p.regain The concept of "Is the useless one useless?"
年, p.regain Isosceles triangle and the length of parallel segments : Origical theorem, : If not segment BC but line BC, : If not isosceles triangle,
年, p.regain Inscribed angle : Starting point, : Two results, : What relationship?, : It becomes quadrangle when showing two results at the same time,
年, p.regain The length of median : Starting point, : Parallelogram and so on, : Triangle, : Two triangles?, : Two triangles?, : Trapezoid, : How about this?, : Hint : looking back, : Hint,
年, p.sample Relationship of interior angle : Triangle, : Quadrangle, : Pentagon, : Quadrangle, : Pentagon,
年, p.sample Quadrangle→Quadrangle : To connect vertexes, : Making by bisector of corner, : Making by perpendicular bisector, : Making by foot of perpendicular,
年, p.sample various points : Development of the wilderness, : To equate areas, : To equate angles,
年, p.sample Equating : Area of triangle, : Area of triangle (2), : Angle of corner,
年, p.sample Can you make? : To make isosceles triangle, : To make square,
年, p.sample Theorem : Theorem of incribed angles, : Two middle points theorem,
年, p.sample Alternative of real thing : Swing, : Swing (2), : Wiper of bus, : Trisection machine of corner?,
年, p.sample Complex Number : Exploring change, : Forming,
年, p.theorem The concept of "Famous Theorems"
年, p.theorem Theorem of Morley : Exproring feature, : Content of theorem,
年, p.theorem Mid points theorem : Content of theorem, : Understaing with track, : Understanding with measurement, : Clue for proof, : Related figure,
年, p.theorem Theorem of incribed angles : Special case, : Combination of special cases, : Understanding with measurement, : Understanding with the other cases,
年, p.theorem Pythagolean theorem : Conjecture, : Measurement (Area of squares), : measurement (Length of sides), : Euclidean additional line and measurement, : Euclidean additional line and "which case the relationship does not exist", : Congruence of triangles,
年, p.theorem Pappus' theorem
年, p.theorem 方べきの定理 : Transformation and conjecture, : Measurement and conjecture, : Specialize and conjecture, : Confirm, : Triangle and proof (1), : Generalization and clasification, : Triangle and proof (2), : Triangle and proof (3),
年, p.theorem Simson's theorem : What is the feature, : Confirm the different cases, : See as the relationship between three points, : See as the transformation of triangle, : See as the change of the area of triangle, : Maximum of the area of triangle, : Area of triangle and circumcenter, : Area of triangle and circle,
年, p.theorem Menelaus' theorem : Observation and conjecture, : Observation and confirm, : Observation,
年, p.theorem Cheva's theorem : Observation and conjecture, : Observation and confirm, : Observation,
年, p.theorem Desargues' theorem : Observation and conjecture, : Secret of three points, : Relationship of three points, : Different cases,
年, p.theorem Euler line : Observation and conjecture, : Observation and conjecture, : Observation and conjecture,
年, p.theorem Newton's theorem (Newton's line) : Observation and conjecture, : Observation and conjecture,
年, p.theorem Newton's theorem : Observation and conjecture, : Observation and conjecture,
年, p.theorem Pappus' theorem : Observation and conjecture, : Observation and conjecture, : Observation and conjecture, : This is not enough,
年, p.theorem Pascal's theorem : Observation and conjecture, : Observation and conjecture, : Observation and conjecture, : This is not enough,
年, p.theorem Feuerbach's theorem : Four circles, : This circle, : Feature of circle (1): Three points circle, : Feature of circle (2): Three points circle, : Six points circle, : Nine points circle,
年, p.transform The concept of "Movement・Transformation"
年, p.transform Point symmetry movement : Exploring freely, : To move a triangle,
年, p.transform axial symmetry : Exploring freely, : To move a triangle, : To move a axis of symmetry,
年, p.transform Parallel displacement : Exploring freely, : To move a triangle,
年, p.transform Rotational movement : Exploring freely, : To move a triangle, : To move the center of rotation,
年, p.transform Complex number (w＝1/z) : Exploring freely, : To move a triangle, : To move a square (1), : To move a square (2),
年, p.transform Complex number (w＝z2) : Exploring freely, : To move a triangle, : To move a circle,
年, p.transform Complex number (w＝(az+b)/(cz+d)) : Exploring freely, : To move a triangle, : To move a circle,
年, p.w_add The concept of "What will occur when something is added?"
年, p.w_add Adding circles to a triangle : It is good to explore with freehand., : Drawing,
年, p.w_add Adding feet of perpendiculars to triangle : It is good to explore with freehand., : Drawing by tool and exploring with moving, : Bonus?,
年, p.w_make The concept of "Can you make it?"
年, p.w_make Making a square (1) : (1), : (2), : (3), : (4), : (5), : (6),
年, p.w_make Making a square (2) : (1), : (2), : (3), : (4), : (5), : (6), : (7), : (8), : (9),
年, p.w_make Making a square(3) : (1)-1, : (1)-2, : (2)-1, : (2)-2, : (3)-1, : (3)-2, : (4)-1, : (4)-2,
年, p.w_make Making a triangle (1) : Right triangle, : Isosceles triangle, : Equilateral triangle,
年, p.w_make Making a triangle (2) : (1), : (1)-2, : (1)-3,
年, p.w_see The concept of "What can you see?"
年, p.w_see Track of circumcenter : Problem, : Example from some students,
年, p.w_see Track of perpendicular bisector : Problem, : Example from students, : Similar problem (1), : Similar problem (2),
年, p.w_see What will appear? : 問題,
年, p.w_see Bisector of corner : On the circle, : On the line,
年, p.w_see Simson's line : P is on the circle, : A line moves, : Track of the line,
年, p.w_w The concept of "Which is which?"
年, p.w_w Circumcenter and barycenter : ,
年, p.w_w Four centroids : ,
年, p.w_w Which is measured? : , : ,
年, p.w_wrong The concept of "Something strange"
年, p.w_wrong Tracks of incenter・excenter : Track of incenter, : Doubt (1), : Track of excenter, : Doubt (2), : Excenter are three., : Incenter and excenter are brothers,
年, p.w_wrong Number of common tangent lines : Starting point, : First result, : Background of the odd number,