Problem and solution essays are a type of argument essay. In these essays, you present a problem and then propose one or more solutions to the problem. These types of essays are common in high school and college writing classes and are often used as part of standardized testing.
There are many potential problem and solution essay ideas, but here are a few potential topics to get you started:
Climate change: One of the biggest problems facing the world today is climate change. In this essay, you could discuss the causes of climate change, the impacts it is having on the planet, and potential solutions to the problem, such as reducing greenhouse gas emissions or implementing renewable energy sources.
Income inequality: Another pressing problem is the growing gap between the rich and the poor. In this essay, you could explore the causes of income inequality, the effects it has on society, and potential solutions such as increasing the minimum wage or implementing a universal basic income.
Cyberbullying: Cyberbullying is a growing problem, particularly among young people. In this essay, you could discuss the causes of cyberbullying, the effects it has on victims, and potential solutions such as educating students and parents about the dangers of cyberbullying and implementing stricter laws and policies to prevent it.
Drug addiction: Drug addiction is a major problem in many communities. In this essay, you could discuss the causes of drug addiction, the effects it has on individuals and families, and potential solutions such as increasing access to addiction treatment and implementing stricter laws to deter drug use.
Environmental degradation: Environmental degradation is another major problem facing the world today. In this essay, you could discuss the causes of environmental degradation, the impacts it has on the planet, and potential solutions such as implementing stricter environmental regulations and promoting sustainable practices.
Remember to support your ideas with strong evidence and to consider the potential pros and cons of each solution you propose. By presenting a well-researched and thoughtfully considered problem and solution, you can help raise awareness and spark important discussions about these pressing issues.
Euclid
Pappus of Alexandria: Book 7 of the Collection. The Elements does not exclusively discuss geometry as is sometimes believed. Elements: his first 28 propositions are those that can be proved without it. History of Mathematics: A Supplement. He therefore would have had some able pupils who may have helped out in writing the books. Works Elements Elements dated to c.
For instance, On Divisions of Figures was a work that focused on geometrical figures. Of course if iii were the correct hypothesis then. There, the Elements became the foundation of mathematical education. The main results of book twelve are that circles are to one another as the squares of their diameters and that spheres are to each other as the cubes of their diameters. One of the many statements that were discovered to be equivalent to the fifth postulate in the course of the many failed attempts to prove it is "Given a straight line, and a point P not on that line, there exists at most one straight line passing through P that is parallel to the given line. It says that when we see objects from a greater angle, those objects appear greater, and that when we see object from a lesser angle, they appear to be lesser. Book six looks at applications of the results of book five to plane geometry.
New Brunswick and London: 978-1-3513-2690-2. They aspired to create a system of absolutely certain propositions, and to them, it seemed as if the parallel line postulate required proof from simpler statements. Introduction To Non-Euclidean Geometry. And finally, when we see things from equal angles, they appear equal. Euclid's Background There is a lot about Euclid's life that is a mystery, including the exact dates of his birth and death, and in many historical accounts he is simply referred to as 'the author of Elements'. No indication is given of the method of reasoning that led to the result, although the Elements. Some scholars have argued that Euclid is — if not exactly a mythical figure — more likely a name given to a group, school, or tradition of ancient mathematicians who developed the fundamentals of geometry.
Other figures, such as lines, triangles, or circles, are named by listing a sufficient number of points to pick them out unambiguously from the relevant figure, e. It was accepted without question by everyone for over 2000 years and there is little evidence which is inconsistent with this hypothesis. Postulate four states that all right angles are equal. The Elements is divided into 13 books. Also, triangles with two equal sides and an adjacent angle are not necessarily equal or congruent. Euclid seems to have known, worked with, or influenced other major Greek figures, including Plato and Archimedes. A 5 16 1 1979 , 190- 200.
Thus an axiomatic system consists of the following: a collection of undefined terms; a collection of definitions; a collection of axioms also called postulates ; and, finally, a collection of theorems. In all probability, it is, next to the Bible, the most widely spread book in the civilization of the Western world. Elements: "Euclid, who put together the Elements, collecting many of c. In fact Euclid was a very common name around this period and this is one further complication that makes it difficult to discover information concerning Euclid of Alexandria since there are references to numerous men called Euclid in the literature of this period. Encyclopedia of Ancient Greece. Thus even mathematics begins with certain unproved assumptions.
Russian , Trudy Sem. These postulates also implicitly assume the existence of points, lines and circles and then the existence of other geometric objects are deduced from the fact that these exist. This collection is a combination of Euclid's own work and the first compilation of important mathematical formulas by other mathematicians into a single, organized format. Euclid's most famous work is his treatise on mathematics The Elements. Postulates Let the following be postulated: 1 To draw a straight line from any point to any point 2 To produce a finite straight line continuously in a straight line 3 To described a circle with any centre and distance 4 That all right angles are equal to one another 5 That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles No. Heath's authoritative translation plus extensive historical research and detailed commentary throughout the text.
Elementary Mathematics from an Advanced Standpoint: Geometry Reprint of 1939 Macmillan Companyed. This may seem "obvious" but it actually assumes that space in homogeneous - by this we mean that a figure will be independent of the position in space in which it is placed. . IV : Euclid Spanish , Mat. Demetrius of Phalerum: Text, Translation and Discussion.
Studies in Logic and the Foundations of Mathematics — The Axiomatic Method with Special Reference to Geometry and Physics Proceedings of International Symposium at Berkeley 1957—8; Reprinted. Translated by Hudoletnjak Grgić, Maja. Euclid is often referred to as the 'father of geometry' and his book Elements was used well into the 20th century as the standard textbook for teaching geometry. The Elements of Euclid and published in colored version in 1847. Due to his groundbreaking work in math, he is often referred to as the 'Father of Geometry'. It has six different parts: First is the 'enunciation', which states the result in general terms i.
