Mathematical proof

the study of plane geometry. This is a type of geometry where math is used to study shapes. The basis of Euclid’s geometry was to prove one thing, and then base the rest of the study of shapes off of the basic proof. He used proofs to prove his ideas about geometry, all based off of the proof that the shortest distance between two points is a straight line. Euclid is still the most widely read Greek author. Egyptian-civilization piArchimedes: One of the greatest mathematicians of all time was…

of Recollection. In the dialogue, Socrates responds by introducing and explaining the Theory of Recollection. By using Meno’s slave as an example, Socrates explained the reason why the slave boy was able to correctly explain the concept of the mathematical/geometrical…

from that of earlier generations and time periods due to the dynamic nature of this field of study. Throughout history, many important individuals have contributed to the field of mathematics and have helped develop the theories, postulates and mathematical rules which are widely accepted today. From the quadratic formula to the trigonometric functions, these people have revolutionized the way we view mathematics in unimaginable ways. Some of these important figures include Pierre…

formal inductive logic proof in Book III, Section 10 of Nicomachean Ethics to conclude, with varying levels of success, that humans who are excessively self-indulgent are no better than animals. Aristotle begins his discussion of moderation by creating his definitions, much like how a logician would define the parameters of their proof. Alluding to his previous definitions of excellence earlier in Book…

Data collected prior to placement such as Oneschool information and previous assessment items assisted in the lesson planning by allowing me to identify not only the students’ academic levels to date, but also note that all students spoke English as their first language, none of the students identified as Aboriginal or Torres Strait Islander and there were no students with disabilities (1.3 - 1.6 AITSL, 2011). The summative assessment for the topic, and curriculum expectations also informed…

We learn that Robert is a prestiged mathematician who was plagued with a rare mental illness. David Auburn hints at the idea that Catherine, Roberts’s daughter, was also gifted with the same mathematical skills as her father. In act 1, Robert and Catherine get into an argument over what are good days or bad days. Catherine seems to believe that the good days are those days when you just stay in bed all day and don’t leave, but Robert believes that those are days lost. Robert shows his concern…

namely those finite sets whose elements are also finite sets, the elements of which are also finite, and so on, is formally equivalent to arithmetic. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite.”…

should have been in a full-time professional care situation,” Catherine disagrees by saying that “he didn’t belong in the nuthouse. He needed to be here. In his own house, near the University, near his students, near everything that made him happy”(Proof I.iv.55, 56-59). The word “nuthouse” indicates Catherine’s contempt and satirical attitude against professional institutions that keep people with mental illness isolated from the community. It is warm family care that counts for the recovery of…

Throughout time, mathematics has always had an influence on society and its ideals. However, the presence of mathematical application is especially present in Plato's The Republic, and especially its effect on mathematical education. Plato's ideas on mathematics education can give reason as to why math influences many other subjects and can encourage critical and abstract thinking in young students. This includes giving students the ability to think abstractly, apply math to all other subjects…

The National Curriculum for Mathematics is an organisational framework which includes a broad set of statutory and non-statutory guidelines that outline what the government deems to be a natural progression in mathematical understanding and knowledge, throughout the primary stage. Although one often considers the curriculum in this way, it is important to consider why and how the curriculum subject matter has been chosen, to which analysing the aims of the curriculum can be a useful starting…