A “proof without words” sounds like a contradiction in terms! How can you prove something if you are not permitted the use of any words? In spite of the seeming absurdity of the idea, the notion of a proof without words — generally shortened to PWW — has acquired great popularity in mathematics in recent decades, and every now and then we come across new, elegant PWWs for old, familiar propositions. In this short article the seemingly contradictory nature of a PWW is discussed, and some examples of PWWs are presented
The way words are used in natural language can influence how the same words are understood by studen...
International audienceIt is commonly admitted that the origin of combinatorics on words goes back to...
Primitive word is a word that can not be represented by any repetition of shorter words. Since every...
Proofs without words are generally pictures, diagrams or schemes that help to see why a given mathem...
From the mid 1970s onwards in almost every issue of the undergraduate mathematics journals Mathemati...
Readers of this magazine may recall that in the December 2012 issue we dwelt on Viviani’s theorem a...
Two themes stand out in this issue: that is proofs without words, or PWWs as they generally reffered...
International audienceThis study seeks to capitalize on the pedagogical potential of visual proof do...
In essence, Computing with Words (CWW) is a system of computation in which the objects of computatio...
The aim of the paper is to study the role and features of proofs in mathematics. Formal and informal...
All the theorems are to be intended with their proof, except if explicitly written wp (that is witho...
Elegance, they say, cannot be defined, merely demonstrated. Mathematics — and mathematicians — can ...
Mathematics is the language of the sciences. Unlike most other scientific laws, mathematical laws ar...
By looking at concrete examples from elementary geometry, we analyse the manner in which the simplic...
We introduce the notion of a set of prohibitions and give definitions of a complete set and a crucia...
The way words are used in natural language can influence how the same words are understood by studen...
International audienceIt is commonly admitted that the origin of combinatorics on words goes back to...
Primitive word is a word that can not be represented by any repetition of shorter words. Since every...
Proofs without words are generally pictures, diagrams or schemes that help to see why a given mathem...
From the mid 1970s onwards in almost every issue of the undergraduate mathematics journals Mathemati...
Readers of this magazine may recall that in the December 2012 issue we dwelt on Viviani’s theorem a...
Two themes stand out in this issue: that is proofs without words, or PWWs as they generally reffered...
International audienceThis study seeks to capitalize on the pedagogical potential of visual proof do...
In essence, Computing with Words (CWW) is a system of computation in which the objects of computatio...
The aim of the paper is to study the role and features of proofs in mathematics. Formal and informal...
All the theorems are to be intended with their proof, except if explicitly written wp (that is witho...
Elegance, they say, cannot be defined, merely demonstrated. Mathematics — and mathematicians — can ...
Mathematics is the language of the sciences. Unlike most other scientific laws, mathematical laws ar...
By looking at concrete examples from elementary geometry, we analyse the manner in which the simplic...
We introduce the notion of a set of prohibitions and give definitions of a complete set and a crucia...
The way words are used in natural language can influence how the same words are understood by studen...
International audienceIt is commonly admitted that the origin of combinatorics on words goes back to...
Primitive word is a word that can not be represented by any repetition of shorter words. Since every...