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#1 Re: This is Cool » Why unit circle? » 2015-12-06 02:48:20

Hi, can anybody tell me if numbers other than natural numbers existed at the time of Euclid?

#2 Re: This is Cool » Why unit circle? » 2015-12-04 07:55:53

Thank you for the response.

Actually, this is the question I searched a lot for. I asked so many people, even last week into my class, from my professor. But unfortunately I couldn't get an answer that can satisfy me. So I'm researching on the web, several notes websites etc, and compiling a set of reasons. I must share here once I'm done. Then I'll discuss them with you great people here.

#3 This is Cool » Why unit circle? » 2015-12-03 20:13:36

Raj.01
Replies: 4

Hi all,

Can anyone help me understanding why we always take unit circle while studying trigonometry? What's the glory of unit circle?

#4 Help Me ! » Suggest me THE BEST Algebra Book » 2015-09-10 18:43:39

Raj.01
Replies: 2

Hi there,

I want to revise all of the basic to advanced level algebra and arithmetic. Please mention a number of few best books that I should study. My basics are very weak. So it'd be great to study them.

#5 Exercises » Found New n Interesting thing about Geometric Points » 2015-08-26 19:27:34

Raj.01
Replies: 2

Hey all,

I searched this topic in Google but I couldn't find anything discussing this topic. This is a pure work of mine. But I don't know if its completely true, somewhat OK or completely a wrong concept.

This is why I'm sharing it here so that you expert guys will share your thoughts on this, resulting in the correction of mine (or anyone else).

<This is a part of a blog post on my personal blog, so I'm just copying the necessary part of my article>

---------------------------------------------------------------------------------------

My Personal Idea

Truly speaking, I didn’t read this anywhere so far. May be someone already discusses this aspect. But still I want to share:

Can you answer what’s zero? Let’s start counting the number of eggs you have in your refrigerator. Suppose, you’ve 3. You eat daily, an egg, then tomorrow, you’ll have 2, then on the day after tomorrow you’ll have one…At the last, you’ll have NO EGG. Now, how you’ll denote this fact mathematically?

To show that we’ve no egg, we will write it that we’ve zero eggs. Zero is basically a number that represents absence of mathematical objects.

Similarly, I feel, a point is to geometry, as Zero is to algebra, empty set is to set theory.

If I ask you, what’s 9 minus 9, what’ll be your answer? Obviously, you’ll say zero.

Similarly, while talking about set theory, if intersection of two or more sets is nothing (empty) we denote this fact by an empty set. Now, physically no empty set exists.

Then I feel, what’s the answer of this geometric problem, a line segment AB minus an equal measure of line segment DE? I’m trying to find the answer of this question, but naturally, I’m inclined to say that it must be a point! Because point has no dimensions, again, a point is to geometry, as zero is to algebra.

Now if you put several zeros on the right of some non zero number, e.g. 9, then it becomes a bigger quantity, e.g. 9,000.

But what about if you put several points together with either one another, or with some line? Obviously, several points together will form a line. Moreover, if you add more points on either to left or right side of a finite line, it’ll start extending indefinitely along left or right direction, respectively (which is one of the five postulates of Euclid).

#6 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-26 16:10:40

hi Bob. Thank you for the book.

Can you answer me one question please? I know that a regular polygon is convex. But if the converse of this true? That is, a convex polygon is regular (in general)?

#7 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-25 17:13:34

Thank you Bob. But the question says, find all solutions. What does it mean? It means that the solution isn't unique?

Also, please tell me a name for a book/eBook that can give me a detailed oriented topics regarding plane figures only e.g. Polygons, their types, properties, theorems regarding them etc.

#8 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-23 22:22:46

I removed this myself.
Reason: The image I couldn't develop.

#9 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-23 20:17:49

Hello Bob, I'm stuck with another problem. I put a lot of time solving it but couldn't do that. Please help me:

Question 157 of Kiselev's Book 1, Compute angles of a triangle which is divided by one of its bisectors into two isosceles triangles. Find all solutions.

#10 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-10 06:12:44

hi Bob, I think so it is something like that what you sketched. While I read the definition of angle from this book's first page, I felt the translator's English wasn't so good. But I'm at the start of this book. if you could recommend some better books, i'll appreciate you.

#11 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-10 02:20:59

Hi all, I'm stuck with this problem "Can sums (differences) of respectively congruent line segments, or arcs, be non congruent? Can sums (differences) of respectively non congruent segments, or arcs be congruent?"

I can't understand the statement. For example, "the sums of two congruent line segments are non congruent (to what?)

Please help me understand the statement. I'm confident I can solve it myself. If you've ideas, please share.

#12 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-09 02:34:19

Actually, truly speaking, my basics were very week when it comes to geometry, so I needed a book to study it in my spare time, so I searched on web and I heard about this book a lot. One interesting thing was that, it was being used as a text book for several decades in various countries. So I picked it up and started studying it. There's not any further reason why I picked it up.

In combination, I've two more book as well, that I keep parallel while studying geometry. But if you know some better book(s), please share with me, I feel much pleasure when I get some interesting books.

#13 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-08 00:58:30

Yeah Bobbym, sure, that's why I joined this forum. smile

#14 Re: Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-07 18:34:31

Hi Bobbym, right now I don't have any issue with some problem and I'm writing the solutions smoothly but it's the way to match my answers with someone else. I've setup a free wordpress blog on this that's dedicated mainly to this book. I don't know if I'm allowed to share it here or not, but I've it on my public profile here.

If someone is interested, I can also copy and paste all those answers here but obviously it'll take a lot of time.

#15 Exercises » Kiselev's Geometry Book 1, Planimetry » 2015-08-07 16:33:22

Raj.01
Replies: 18

Hi all. Does somebody know any source from where we can get the solutions to exercises of this book? Or at least, we could get proper hints or answers to selected odd numbered problems? I've started reading this book and exercises look me really technical. So I thought to solve all of these problems. I've started from Introductory chapter and its exercises.

People with similar interest are warmly welcome to join me here so that we can share ideas or match our answers, that's a recommendation from the author of this book. Waiting for your replies.

Thank you,
Raja.

#17 Introductions » A new math lover, just joined the forum. » 2015-08-07 09:13:23

Raj.01
Replies: 12

Hello all,

I'm Ghufran, a student of Master of Mathematics from RIPHAH Intl. University, Islamabad, Pakistan. I'm here to introduce myself in front of all forum fellows. I'm 24 years old male, learning new math tactics everyday. Hoping to be very warmly welcomed in this forum.

Cheers,
Raja

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