Since the focus of this site is to provide educational materials to students, teachers in particular and schools in general, this author deem believe that the security of educational institutions should at the top-level priority of school administrators.
An isosceles triangle is a triangle with two sides equal in length just like the photo below.
Isosceles Triangle
Let the base angle of the isosceles triangle = 2r.
Let (line-AB) = c, (line-BC) = a, (line-AC) = b, Let (line-AD) = d
for isosceles triangle, c = a.We are asked to solve for b.
S1 = (1/2)cdsin(r)
S2 = (1/2)bdsin(r)Therefore
(S1/S2) = c/b (1)
or c*c = (b*b)(S1*S1)/(S2*s2) (2)
The perimeter of the triangle
p = 2c + b
The semiperimeter s = (1/2)p = c + (1/2)bs-a = (1/2)b
s-c = (1/2)b
s-b = c – (1/2)bthe total area of the triangle
S1 + S2 = SQRT[s(s-a)(s-b)(s-c)]
= SQRT{[c + (1/2)b]*(1/2)b*(1/2)b*[c - (1/2)b]}
= (1/2)b*SQRT[c*c - (1/4)b*b] (3)Square both sides of (3), substitute (2) into (3) and rearrange
The answer:
(line-AC) = b = 2*SQRT[S2*(S1+S2)]/SQRT{SQRT[4*S1*S1 - S2*S2]}
Squaring a number below 13 is still an easy task. But how can you find the square of a large number, say 53, in a few seconds? Want to know the technique? Watch the tutorial
If you are interested in learning how to multiply using Vedic Mathematics, then watch the tutorial video below:
Simplifying radicals is relatively easy. However, students in high school and college find it a little more difficult simplifying large radicals. Learn the technique in simplifying large radicals by watching the video:
In college, we have studied Fibonacci sequence in Algebra, Number Theory, Calculus and other subjects. However, Fibonacci sequence has been dealt with more focus in Number Theory – a field of mathematics dealing with the study of numbers, sequences, number patterns and theories regarding the development of numbers and equations.
According to wikipedia, in mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. Fibonacci’s 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics.
The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc. In mathematical terms, it is defined by the following recurrence relation:
That is, after two starting values, each number is the sum of the two preceding numbers. The first Fibonacci numbers (sequence A000045 in OEIS), also denoted as Fn, for n = 0, 1, 2, … ,20 are:
| F0 | F1 | F2 | F3 | F4 | F5 | F6 | F7 | F8 | F9 | F10 | F11 | F12 | F13 | F14 | F15 | F16 | F17 | F18 | F19 | F20 |
| 0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 | 377 | 610 | 987 | 1597 | 2584 | 4181 | 6765 |
Every 3rd number of the sequence is even and more generally, every kth number of the sequence is a multiple of Fk.
The sequence extended to negative index n satisfies Fn = Fn?1 + Fn?2 for all integers n, and F?n = (?1)n+1Fn:
.., ?8, 5, ?3, 2, ?1, 1, followed by the sequence above.
Mathematics is all about spotting patterns, finding the underlying logic in the seemingly random and chaotic world around us; and using this information to predict future behaviour. Traditionally maths has been used to make predictions about inanimate objects, like the orbit of planets or the weather. But as Stephen Baker explains in The Numerati, mathematicians are increasingly turning their attention to human behaviour. What if those strings of numbers are records of the things you’ve bought, places you’ve travelled to, websites you’ve visited, parties you’ve voted for? Find the pattern in the numbers and mathematicians will be able to predict – with surprising accuracy – what your next move will be. The ‘numerati’ is the name Baker gives to the group of latterday fortune-tellers whose job it is to decode our behaviour. His book explores the lives of such people and attempts to analyse how powerful they have become…
Ok, I am starting to give lectures on some topics in Algebra (Prime Numbers and and its definition). These are preliminary lectures or tutorials in mathematics. Discussing these math concepts is very important to further studies in math. This is the reason why I will be publishing more tutorials like this before posting more articles on how to solve math word problems.
A prime number (or prime for short) is a natural number (from positive 1 to positive infinity which is usually symbolized by the capital letter “N” in most math books and other references) that can only be wholly divided by 1 and itself. For theoretical reasons, the number 1 is not considered a prime (we shall see why later on in this chapter). For example, 2 is a prime, 3 is prime, and 5 is prime, but 4 is not a prime because 4 divided by 2 equals 2 without a remainder.
As part of my series to teach readers, especially students, to solve math word problems or word problems in math, I am starting that series with some tips on how to approach word problems. Let me give you some proven and tested ways to solve word problems especially in Algebra and standardized tests.
If you have studied geometry, it is highly improbable that you have not encountered the name Euclid. Euclid is a mathematician who is is generally considered as the father of geometry. Euclidean geometry is a field of geometry (non-Euclidean geometry is another field) where plane geometry is studied. When we say plane geometry, we refer to all concepts pertaining to points, lines and plane.
But who is Euclid? Find out below:
In this site, I intend to upload free math softwares ready for download. These games will include Sudoku, Tower of Hanoi, Domino and other games. Also, some mathematical analyses will be made on the probability of winning in these games.
Card games, tile games and puzzles will likewise be featured in this site so watch out for these. 
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