Can you post some interesting, philosophical, mathematics concepts that I can ponder?

Answer 1

i am sure you are familiar with paschals triangle, why are the numbers = to the powers of eleven

1 =11^0
11 =11^1
121 =11^2
1331 =11^3


why are these co-effecients of the polynomial equation related to the powers of 11, and explain the further progression

Answer 2

The Monty Hall Problem

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Because there is no way for the player to know which of the two unopened doors is the winning door, many people assume that each door has an equal probability and conclude that switching does not matter. However, as long as the host knows what is behind each door, always opens a door revealing a goat, and always makes the offer to switch, opening a losing door does not change the probability of 1/3 that the car is behind the player's initially chosen door. As there is only one other unopened door, the probability that this door conceals the car must be 2/3. It is therefore to the contestant's advantage to switch to door 2.

Answer 3

i might prefer to confirm the concept of Inertia. I are attentive to it is likewise a concept of Classical Physics because it describes the action of count and how that's stricken by ability of utilized forces. that's sturdy stuff nonetheless, because it could additionally help in different instructions as nicely. i presumed i might look at the concept on the subject of your question. Inertia originates from Latin and it ability idle or lazy. Sir Issac Newton's First regulation of action pronounced that an merchandise which isn't in action will stay at relax till some rigidity motives it to circulate. Newton considered that there are variables to evaluate in this subject, such as Gravity and Friction. Nicolaus Copernicus had argued that we are continuously in action by way of fact the Earth spins and travels through area. I even have considered your question and as I see a potential difficulty there, I even have attended to that still. difficulty: A professor desires to motivate scholars to do the mandatory artwork in her Philosophy classification. G = Gravity = the student's own might desire to bypass the direction F = Friction = any form of adverse consequences the student will acquire for no longer actually discovering the mandatory expertise set. S = success = useful flow on the area of the student furnish a reaction that displays the student's expertise and expertise of the direction textile. while G + F = S the Professor is happy. in spite of the shown fact that, while G + F does no longer = S....might or no longer it particularly is an greater handy answer for the Professor to discover the thank you to velocity up the Earth fairly than cope with the myriad of variables that scholars recent of their individual efforts to maintain Inertia.

Answer 4

Where do mathematics and philosophy meet? Is there a problem in mathematics which can be answered in philosophy? Is there a problem in philosophy which can
be answered in mathematics? Are there problems on the
boundary which can be answered in either discipline?
Could philosophy bypass the limits of mathematical
formalisms without contradicting Godel's theorem?

Answer 5

Have you heard of Fermats last theorem ?

we all know the pythagoras theorem where if the sides are a and b in a right angled triangle and the hypotenuse is c

then a^2 + b^2 = c^2

but Fermat (in 18th century i suppose.....) proved that it is not true for any power except 2 in a right angled triangle. But he wrote in his diary that.....the margin in my book is too small to contain the proof of this theorem..

How unfortunate !

Cause nobody has been able to prove that since......

(Some ppl claim to have solved the problem.......)

Why dont u search wiki for "Fermat's Last Theorem" ?

Answer 6

Godel's Theorem:

Any system of logic strong enough to encompass number theory is either inconsistent or incomplete.

Stated differently: Either all of mathematics is false or there are truths of mathematics that are impossible to prove.

When it was first proved, many mathematicians were shocked to discover that there were truths of mathematics that are impossible to prove. I had the opposite reaction. I was shocked to realize that we have to accept that mathematics works based on faith -- not reason.