Sophisms are closely related to paradoxes. Both assume the form of a statement that contradicts your intuition. In case of a sophism, your intuition is right in telling you that the statement is wrong

Consider a rectangle ABCD and a parallelogram EFGH with the same base length and height. Let us cut the rectangle ABCD into infinitely many infinitely thin strips: lines, which fill the whole area of the

Taking derivatives from both sides of a valid equation we obtain Dividing both sides by x, we must conclude that 2 = 1. For other sophisms check out my other posts.

Time is infinite. Your life is finite. Consequently, the probability of you being alive at this particular moment is zero. ... and yet you are alive! For other sophisms see my other posts.

As we know from physics, the amount of work done is proportional to power applied and the time spent: Work = Power × Time Substituting into this formula the well-known equations Knowledge = Power, Time

Consider an arbitrary triangle ABC. Let G be the midpoint of AB and let D be the intersection of the midpoint perpendicular of AB with the bisector of ∠C. Drop perpendiculars DE and DF to the sides AC

For other sophisms check out my other posts.

Bart's Cookie Store is selling two types of cookies - vanilla and chocolate. Vanilla cookies sell at $1 per three pieces, while chocolate ones sell at $1 per two. At the beginning of the day Bart had 30

Consider the following statement: This whole statement is true if and only if the Earth is flat Let us denote the whole statement by A. Note that we can then rewrite it a bit more formally as the following

The Liar's Paradox is perhaps the shortest sophism there is. In its most common form it fits in just four words: This sentence is false. Think about it: if the sentence is indeed false, then we should

Edit: Originally this post was named "Sophisms: Table of Contents" and was intended to be a single, regularly updated, table of contents for all the sophisms I'm posting here because I've just

Number one may be represented as an infinite continued fraction as follows: Number two may also be represented in exactly the same way: Consequently, we should conclude that 1 = 2. Please, avoid posting

Consider again three arbitrary numbers a, b, c, such that a+b = c Then: (3a-2a)+(3b-2b) = (3c-2c) Reorganize and simplify: 3a+3b-3c = 2a+2b-2c 3(a+b-c) = 2(a+b-c) 3 = 2 QED. Note that you may use the same

Sophisms come in various shapes and sizes. Some are simple mathematical "find-the-mistake" puzzles. Others are subtle observations, requiring whole theories to resolve them. Some are deeply

Homer threw a baseball to Bart. Like that: Notice that at the moment in time depicted on the image, the ball is located at a certain fixed position in space. While it is being in that fixed position, it

One sunny Monday morning Homer decided to go to his favourite bar to get a can of beer. Right before leaving the house, he paused to think for a moment: "The bar is located 1km away. If I start walking

Zeno's paradoxes are among the most ancient and famous sophisms known to date. They are thought to be proposed (or collected) by the ancient greek philosopher Zeno in the V century BC. At least nine known

Consider two arbitrary numbers a and b. Let a + b = 2c Rearrange this in two ways to get two new valid equations: a - 2c = -b a = -b + 2c Multiply the corresponding sides of the two equations: a2 - 2ac

Let a, b, and c be arbitrary numbers, such that a = b + c Multiply both sides of the equation by (a-b) and open the brackets: a(a-b) = (b+c)(a-b) a2 - ab = ab + ac - b2 - bc Move ac to the left and extract:

Homer entered a bar. -- What beers do you serve here? -- Guinness at $3 a can, and Duff at $5, - answered the barman. Homer feverishly searched his pocket, scraping together $3 in small coins. He passed