Developing shift problems to foster geometrical proof and understanding

2013 ◽  
Vol 32 (2) ◽  
pp. 142-159 ◽  
Author(s):  
Sonia Palha ◽  
Rijkje Dekker ◽  
Koeno Gravemeijer ◽  
Bernadette van Hout-Wolters
Keyword(s):  
Geometrical Proof

2. Note on a Geometrical Theorem

1878 ◽  
Vol 9 ◽  
pp. 533-536
Author(s):  
Tait
Keyword(s):  
The Other ◽  
Geometrical Proof ◽  
In Trans ◽  
The Mean ◽  
Concentric Circles ◽  
Confocal Conics

In “Trans. R.S.E.” (1864–5) Fox Talbot proved very simply, by means of a species of co-ordinates depending on confocal conics, the following theorem, at the same time asking for a simple geometrical proof.If two sets of three concentric circles, with the same common difference of radii, intersect one another—the chords of the arcs intercepted on the mean circle of each series by the extremes of the other are equal.

scholarly journals Geometrical Proof of tan A + tan B + tan C = tan A tan B tan C

1916 ◽  
Vol 20 ◽  
pp. 231-232
Author(s):  
Colin Kesson
Keyword(s):  
Geometrical Proof ◽  
Image Position

Let ABC be the Δ, AD ⊥ to BC produced to meet circumcircle in K, BL a diameter of circumcircle, LM ⊥ to AK. Let BK, KG, CL and LA be joined.

scholarly journals On Desargues Theorem

1944 ◽  
Vol 34 ◽  
pp. 17-19
Author(s):  
J. H. M. Wedderburn
Keyword(s):  
Analytical Methods ◽  
Geometrical Proof ◽  
Analytical Proof ◽  
Desargues Theorem ◽  
Degenerate Cases

The usual proofs of Desargues Theorem employ either metrical or analytical methods of projection from a point outside the plane; and if it is attempted to translate the analytical proof by the von Stuadt-Reye methods, the result is very long and there is trouble with coincidences. It is the object of this note to give a short geometrical proof which, in addition to the usual axioms of incidence and extension, uses only the assumption that a projectivity which leaves three points on a line unchanged also leaves all points on it unchanged. Degenerate cases are excluded as having no interest.

scholarly journals Geometrical proof that tan x tan y + tan y tan z + tan z tan x= 1 when x + y + z = 90°

1916 ◽  
Vol 20 ◽  
pp. 237-238
Author(s):  
G. E. Crawford
Keyword(s):  
Geometrical Proof ◽  
Image Position

H being the orthocentre of a triangle ABC, we may call the angles HAC, HBA, HCB = x, y, z respectively, for their sum is 90°.Now tan x tan z = ∴ tan x tan z + tan z tan y + tan x tan y = 1.

82.31 A Geometrical Proof of a Trigonometric Inequality

1998 ◽  
Vol 82 (494) ◽  
pp. 278
Author(s):  
Taichi Maekawa
Keyword(s):  
Geometrical Proof
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