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47,590
by congruent triangles
, 2001
"... Abstract. We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure poin ..."
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Abstract. We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], a ..."
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Cited by 25 (20 self)
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This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8, 10, 3, 12, 5] among other places; the most comprehensive survey currently available is [12]
On the Perimeter of the Intersection of Congruent Disks
 BEITRAGE ZUR ALGEBRA UND GEOMETRIE CONTRIBUTIONS TO ALGEBRA AND GEOMETRY VOLUME 47 (2006), NO. 1, 5362.
, 2006
"... Almost 20 years ago, R. Alexander conjectured that, under an arbitrary contraction of the center points of finitely many congruent disks in the plane, the perimeter of the intersection of the disks cannot decrease. Even today it does not seem to lie within reach. What makes this problem even more i ..."
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Cited by 1 (0 self)
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Almost 20 years ago, R. Alexander conjectured that, under an arbitrary contraction of the center points of finitely many congruent disks in the plane, the perimeter of the intersection of the disks cannot decrease. Even today it does not seem to lie within reach. What makes this problem even more
BUBBLES OF CONGRUENT PRIMES
"... Abstract. In [15], Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu’s theorem to imaginary quadratic fields, where we prove the existence of “bubbles ” containing arbi ..."
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Abstract. In [15], Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu’s theorem to imaginary quadratic fields, where we prove the existence of “bubbles ” containing
Correctness Is Congruent with Quality
, 1990
"... Introduction This note was prompted by Bradley J. Brown's article in the April 1990 SEN titled "Correctness Is Not Congruent With Quality." In his article, the author argues that software correctness is sometimes desirable and sometimes undesirable. I claim that correctness is the mo ..."
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Introduction This note was prompted by Bradley J. Brown's article in the April 1990 SEN titled "Correctness Is Not Congruent With Quality." In his article, the author argues that software correctness is sometimes desirable and sometimes undesirable. I claim that correctness
CONGRUENT NUMBERS AND ELLIPTIC CURVES
"... Abstract. These are essentially the lecture notes from a section on congruent numbers and elliptic curves taught in my introductory number theory class at the Ohio State University spring term of 2007. The students in this class were assumed to only have a basic background in proof theory (such as ..."
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Abstract. These are essentially the lecture notes from a section on congruent numbers and elliptic curves taught in my introductory number theory class at the Ohio State University spring term of 2007. The students in this class were assumed to only have a basic background in proof theory (such
Hidden Congruent Deduction
"... Proofs by coinduction are dual to proofs by induction, in that the former are based on a largest congruence, and the latter on a smallest subalgebra (e.g., see [12]). Inductive proofs require choosing a set of constructors, often called a basis; the dual notion is cobasis, and as with bases for indu ..."
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Proofs by coinduction are dual to proofs by induction, in that the former are based on a largest congruence, and the latter on a smallest subalgebra (e.g., see [12]). Inductive proofs require choosing a set of constructors, often called a basis; the dual notion is cobasis, and as with bases for induction, the right choice can result in a dramatically simplified proof. An interesting complication is that the best choice may not be part of the given signature, but rather contain operations that can be defined over it.
THE CONGRUENT NUMBER PROBLEM
"... A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include Pythagorean triples like (3, 4, 5). We can scale such triples to get other rational right triangles, like (3/2, 2, 5/2). Of course, usually when two sides are ratio ..."
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A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include Pythagorean triples like (3, 4, 5). We can scale such triples to get other rational right triangles, like (3/2, 2, 5/2). Of course, usually when two sides are rational the third side is not rational, such as the (1, 1, √ 2) right triangle.
Ventral intraparietal area of the macaque: congruent visual and somatic response properties
 J. Neurophysiol
, 1998
"... 1998. In a previous report, we described the visual response proper Poranen 1974; Leinonen and Nyman 1979), and premotor ties in the ventral intraparietal area (area VIP) of the awake macortex (Rizzolatti et al. 1981). caque. Here we describe the somatosensory response properties in area VIP and th ..."
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Cited by 89 (3 self)
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1998. In a previous report, we described the visual response proper Poranen 1974; Leinonen and Nyman 1979), and premotor ties in the ventral intraparietal area (area VIP) of the awake macortex (Rizzolatti et al. 1981). caque. Here we describe the somatosensory response properties in area VIP and the patterns of correspondence between the responses The posterior parietal cortex contains several distinct areas of single neurons to independently administered tactile and visual that are part of the dorsal stream visual pathway (Ungerleider stimulation. VIP neurons responded to visual stimulation only or and Mishkin 1982). One of these is the ventral intraparietal to visual and tactile stimulation. Of 218 neurons tested, 153 (70%) area (VIP), located in the deepest portions of the intrapariewere bimodal in the sense that they responded to stimuli that were tal sulcus, which receives a major source of visual input independently applied in either sensory modality. Unimodal visual from the middle temporal area (MT) in the superior temporal and bimodal neurons were intermingled within the recording area sulcus (Maunsell and Van Essen 1983; Ungerleider and Deand could not be distinguished on the basis of their visual response simone 1986). Consistent with this input, we have shown properties alone. Most of the cells with a tactile receptive field that neurons in area VIP display response properties that are (RF) responded well to light touch or air puffs. The distribution
Results 1  10
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47,590