Probabilistic verification of elementary geometry statements

1997 ◽  
pp. 87-101 ◽  
Author(s):  
Giuseppa Carrá Ferro ◽  
Giovanni Gallo ◽  
Rosario Gennaro
Keyword(s):  
Elementary Geometry ◽  
Probabilistic Verification

scholarly journals An Inhomogeneous Minimum For Non-Convex Star-Regions With Hexagonal Symmetry

1955 ◽  
Vol 7 ◽  
pp. 337-346 ◽  
Author(s):  
R. P. Bambah ◽  
K. Rogers
Keyword(s):  
Quadratic Form ◽  
Binary Quadratic Form ◽  
Elementary Geometry ◽  
Hexagonal Symmetry ◽  
Real Numbers ◽  
Inhomogeneous Minimum ◽  
Image Position ◽  
Indefinite Binary Quadratic Form

1. Introduction. Several authors have proved theorems of the following type:Let x0, y0 be any real numbers. Then for certain functions f(x, y), there exist numbers x, y such that1.1 x ≡ x0, y ≡ y0 (mod 1),and1.2 .The first result of this type, but with replaced by min , was given by Barnes (3) for the case when the function is an indefinite binary quadratic form. A generalisation of this was proved by elementary geometry by K. Rogers (6).

scholarly journals Two Points in the Teaching of Elementary Geometry

1932 ◽  
Vol 16 (217) ◽  
pp. 64
Author(s):  
Alfred Lodge
Keyword(s):  
Elementary Geometry

scholarly journals On the number of conditions determining geometrical figures

1884 ◽  
Vol 3 ◽  
pp. 22-29
Author(s):  
A. Y. Fraser
Keyword(s):  
First Principles ◽  
Elementary Geometry ◽  
Special Cases ◽  
Plane Polygon

This paper is an attempt (I) to deduce from first principles the number of conditions required to determine a plane polygon of n sides; (II) thence to deduce the numbers for special cases; and (III) to discuss the effects of a redundancy and a deficiency in the number of conditions. An investigation of this kind should form an important as well as interesting accompaniment to the ordinary study of elementary geometry.

scholarly journals DEFS—Data Exchange with Free Sample Protocol

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1455
Author(s):  
Rafael Genés-Durán ◽  
Juan Hernández-Serrano ◽  
Oscar Esparza ◽  
Marta Bellés-Muñoz ◽  
José Luis Muñoz-Tapia
Keyword(s):  
Data Exchange ◽  
Digital Data ◽  
Smart Contracts ◽  
Probabilistic Verification ◽  
Real Dataset ◽  
The Real ◽  
Building Trust ◽  
Free Sample ◽  
Random Samples ◽  
Main Ideas

Distrust between data providers and data consumers is one of the main obstacles hampering the take-off of digital-data commerce. Data providers want to get paid for what they offer, while data consumers want to know exactly what they are paying for before actually paying for it. In this article, we present a protocol that overcomes this obstacle by building trust based on two main ideas. First, a probabilistic verification protocol, where some random samples of the real dataset are shown to buyers in order to allow them to make an assessment before committing any payment; and second, a guaranteed, protected payment process enforced with smart contracts on a public blockchain that guarantees the payment of data if and only if the provided data meet the agreed terms, and that honest players are otherwise refunded.

scholarly journals Safe domain and elementary geometry

2004 ◽  
Vol 25 (6) ◽  
pp. 835-844 ◽  
Author(s):  
Jean-Marc Richard
Keyword(s):  
Elementary Geometry
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