Pascal's triangle

The theorem used to find the hypotenuse, adjacent, or opposite sides of a triangle is also used in Euclidian Geometry. “A” squared plus “B” squared equals “C” squared is the formula used in the theorem. For example, we are given two numbers in the sides of a triangle; if we are given the adjacent and opposite sides, and we must figure out the hypotenuse, we will be required to use the Pythagorean Theorem. The two numbers…

Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It does not tell us exactly which right triangle to draw.…

non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic lemmas, one is on the fact “Among all the pedal’s…

The sculptural portrait of Faustina the Elder is made of marble and was sculpted between the years of 140 and 160 A.D. She is a Roman piece by an unknown artist, and is housed in the Getty Villa. Faustina is composed of strong lines and shapes to draw the viewer into the vertical dominant composition. Multiple forms break down into triangular shapes that bring the eye up and down the length of the piece, in order to add some movement to her otherwise static pose. Faustina the Elder stands…

against the existence of God. This wager which will result in either heaven, hell, or no consequence. Based on Pascal’s premises, I believe his argument is unsound. This paper will be divided into three sections in which I will discuss my evaluation of Pascal’s Wager. In Section One, I will briefly summarize Pascal’s argument. In Section Two, I will make an argument in support of Pascal’s argument being unsound. In Section Three, I will address a possible objection to my argument. Section One…

Blaise Pascal’s basic belief was that all people have to just take a 50/50 wager for the existence of God. His claim comes from his belief that there is no reasonable way to support either side of the argument about the existence of God. Although Blaise Pascal was a brilliant French philosopher, mathematician and physicist, his claim that there is no creditable evidence to support a reasonable belief about God is not completely correct. It is just an easy way to completely avoid an intelligent…

The Ontological Argument and Pascal’s Wager The “Ontological Argument” was created by Saint Anselm; this argument is in support of God’s existence. His argument is one based on observation and reason not on empirical evidence and is spit in to three parts. The parts include why god exists, why god cannot be thought to not exist, and lastly why atheists are able to think that God does not exist. In the first section he begins with a definition of God that he believes everyone would be accepting…

This essay will address whether if I agree or disagree to Pascal’s claim about man. In his famous essay on the Wager, Pascal claims that ‘Man is dignified, despite his vulnerabilities’. The concept of dignity means the quality or state of being worthy of respect and honor whereas vulnerability deals with being easily hurt, in other words, being weak. Pascal thought ‘Man is dignified, despite his vulnerabilities’ because he thought that people should live by believing that god exists and if a man…

Another proof of God is known as the Ontological argument which was thought up by the great St. Anselm. The word ontological means analyzing one’s nature of being and simply asking if it is real. The Ontological argument proofs include: (1) Assume that GCB (greatest consumable being) does not exist in reality, but in the mind alone; (2) Existence in reality is greater than existence in the mind alone; (3) It is possible the GCB exists in reality; (4) In such of a case, GCB would be greater than…

What is Pascal 's Wager? Do you agree that betting on the existence of God is most prudent option? Why? Pascal’s Wager can be briefly summed up as that there is no reason not to believe in God, because you stand to lose nothing by believing in Him. This rational way of thinking about the existence of God is quite interesting. It almost seems to suggest that…