This document explains some common mathematical concepts that may be unintuitive or mysterious. It begins by stating that some math concepts taught in primary and secondary school may not be fully understood at that age. It then provides explanations for several concepts: - Pi is an irrational number that cannot be expressed as a ratio of integers and whose value is approximated, not equal to 7/22. - The value of X0 is 1, not 0, which can be understood through limits and calculus. - Multiplying two negative numbers results in a positive value, which is counterintuitive but can be explained through an example using subtraction.

1. Some Mysteries of
Mathematics Explained
by
Aurora Computer Studies
(auoracs.lk)
Aurora Computer Studies 1

2. Introduction
• Some of the mathematics concepts are
taught at primary or secondary school
• Our intellectual capacity may not have built
enough to fully understand some aspects of
mathematics at that time
• Now is the time to revisit and understand
because mathematics is not a mystery, but
a rational formal science subject
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3. Value of ∏ is 7/22
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4. Explanation - ∏
• The value of ∏ is not 7/22. It is just an
approximation !
• ∏ = 3.141 592 653 589 793 238 462
643 383 279 502 884 197 169 399
375 105 820 974 944 592 307 816
406 286 ...............
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5. Explanation - ∏
• ∏ is an irrational number
• Irrational numbers can not be
expressed as ratio of integers
o Other common irrational numbers are;
• 2 , e (Euler’s number), φ (The golden ratio), ….
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6. Explanation - ∏
• Mathematicians have developed different
ways to calculate the approximate value of
∏;
o Measuring circumference
of circles
o Using Polygons to approximate
o Using infinite series
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7. X0
= 1
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8. Explanation - X0
• Your natural instincts may say that X0
must be 0
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X (say 10) Xn
103
10X10X10 =1000 (3 times 10)
102
10X10 = 100 (2 times 10)
101
10 (1 times 10)
100
0 ?? (0 times 10)

9. Explanation - X0
• lim
𝑥→0
𝑁 𝑥
= 1
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N Nx
103
1000
102
100
101
10
100.1
1.258925….
100.01
1.023292….
100.001
1.002305…
……
100.0000000001
1.00000000023….

10. Explanation - X0
• When you closely analyze the trend,
now you should see that though it
looks counter intuitive X0
= 0 is valid.
o If you are still a bit confused, time to learn about
calculus and the concept of limits in advanced
mathematics.
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11. Multiplication of two
negative numbers is a
positive value.
(-a) X (–b) = ab
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12. Explanation - (-a) X (–b) = ab
• The following can be explained easily
o A + B
o A + (-B)
o (-A) + (-B)
o A X B
o A X (-B)
o But (-A) X (-B) = AB is somewhat counter intuitive and
difficult to understand at first.
• So you may have took it for granted (or believe)
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13. Explanation - (-a) X (–b) = ab
• Following is an explanation using an
example;
-5 X 0 = 0
-5 X (3 – 3) = 0
(-5X3) + (-5 X -3) = 0
-15 + (-5 X -3) = 0
In order for this to be true or consistent with other
concepts (-5 X -3) must be +15
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14. References
• Irrational numbers
o https://www.mathsisfun.com/irrational-numbers.html
• Introduction to limits
o http://www.mathsisfun.com/calculus/limits.html
• Pi
o https://en.wikipedia.org/wiki/Pi
• Why is negative into negative is positive?
o https://www.youtube.com/watch?v=rK4sXm_MPWo
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15. Thank You !
Presented by
Nalaka Gamage
Aurora Computer Studies
(auoracs.lk)
15

16. You may also interested
• A simple guide to maths
o https://www.slideshare.net/auroracslk/a-simple-guide-
to-mathematics
• Three types of maths people
o https://www.slideshare.net/auroracslk/how-people-
use-maths
• Critical thinking
o https://www.slideshare.net/auroracslk/ss-73024682
Aurora Computer Studies (auroracs.lk) 16

17. "We are what we repeatedly do.
Excellence, then, is not an act,
but a habit."
~ Aristotle.
Aurora Computer Studies (auroracs.lk) 17

18. What courses do we offer?
• AL ICT (English & Sinhala medium)
o http://auroracs.lk/al-ict/
• BIT – UCSC Degree
o http://auroracs.lk/bit/
• BCS
o http://auroracs.lk/bcs/
Aurora Computer Studies (auroracs.lk) 18

19. Premier Study Center
Aurora Computer Studies,
Summerset College,
# 135, 3rd Floor,
DFCC Building,
High Level Road,
Maharagama.
City Study Center
Aurora Computer Studies,
Summerset College,
# 88/2, 2nd Floor,
BOC Building,
High Level Road,
Kirulapone, Colombo 06
Details and enquiries :
Call - 0719 842030
E-mail – info@auroracs.lk
Web - www.auroracs.lk
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