Often you might have observed - we won't forget many events that occurred in our life. Our brain recalls significant / important / worst events in our life even after many years. Our brain does not forget many events that we experienced in life. In many cases visualization is equivalent to one kind of experiencing. Visualizing math means experiencing it. Our brain mainly thinks in terms of pictures. Example - When someone speaks about the ocean, the rough picture of galaxy, universe or ocean may appear in our brain. When someone speaks about infinity, then ocean or our galaxy may appear in people's mind. Our brain tries to understand infinity with help of these things. Thus picture are more closure to the brain. Our brain understand the fact, subject easily expressed by pictures. That’s why it is said that "one picture is worth more thousand words ". Advantages of Visual Mathematics 1) Get better conceptual understanding, clarity. 2) Promotes creativity. 3) Makes math learning faster. 4) Develop insight & vision in students. 5) Develops number sense. This book tries to explain essential math concepts by practical examples & visual pictures. Due to this learning math becomes enjoying process. Visualization of math concept through picture play vital role. Visual learning is stress less learning. Techniques of visual learning develop insight in student. It’s the eyes with insight that can look beyond in mathematics. “Person can look beyond if it has vision & insight. Visual math increases insight. " ~ Vitthal B. Jadhav (Mathematician / Lyricist) For more book by author refer https://play.google.com/store/books/author?id=Vitthal+B.+Jadhav

1. Power of
Looking beyond by improving insight
VITTHAL B. JADHAV
Visual Math is Key to Learn Math without Stress

3. Preface
Often you might have observed - we won't forget many events that
occurred in our life. Our brain recalls significant / important / worst events in
our life even after many years. Our brain does not forget many events that we
experienced in life. In many cases visualization is equivalent to one kind of
experiencing. Visualizing math means experiencing it. Our brain mainly thinks
in terms of pictures. Example - When someone speaks about the ocean, the
rough picture of galaxy, universe or ocean may appear in our brain. When
someone speaks about infinity, then ocean or our galaxy may appear in people's
mind. Our brain tries to understand infinity with help of these things. Thus
picture are more closure to the brain. Our brain understand the fact, subject
easily expressed by pictures. That’s why it is said that "one picture is worth
more thousand words ".
Advantages of Visual Mathematics
1) Get better conceptual understanding, clarity.
2) Promotes creativity.
3) Makes math learning faster.
4) Develop insight & vision in students.
5) Develops number sense.
This book tries to explain essential math concepts by practical examples &
visual pictures. Due to this learning math becomes enjoying process.
Visualization of math concept through picture play vital role. Visual learning is
stress less learning. Techniques of visual learning develop insight in student. It’s
the eyes with insight that can look beyond in mathematics.
“Person can look beyond if it has vision & insight.
Visual math increases insight. "
~ Vitthal B. Jadhav
(Mathematician / Lyricist)

4. 13 । Power of ‘Visual Mathematics’ Copyright © 2018 by Vitthal B. Jadhav
13 । Power of Visual Mathematics
VISUALIZING SUM of ODD NUMBERSVISUALIZING SUM of ODD NUMBERSVISUALIZING SUM of ODD NUMBERSVISUALIZING SUM of ODD NUMBERS
1
1 = 12
1 3 5 7
1 2 4 6
1 2 3 5
1 2 3 4
1 + 3 + 5 + 7 = 42
….
….
1 3 5 7 9 11 13 15
1 2 4 6 8 10 12 14
1 2 3 5 7 9 11 13
1 2 3 4 6 8 10 12
1 2 3 4 5 7 9 11
1 2 3 4 5 6 8 10
1 2 3 4 5 6 7 9
1 2 3 4 5 6 7 8
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 82
In general,
1 + 3 + 5 + 7 + … + (2n - 1) = n2
1 3
1 2
1 3 5
1 2 4
1 2 3
1 3 5 7 9
1 2 4 6 8
1 2 3 5 7
1 2 3 4 6
1 2 3 4 5
1 2 3 4 5
1 + 3 + 5 = 32
1 + 3 = 22
1 + 3 + 5 + 7 + 9 = 42

5. 14 । Power of ‘Visual Mathematics’ Copyright © 2018 by Vitthal B. Jadhav
14 । Power of Visual Mathematics
VISUALIZING SUM ofVISUALIZING SUM ofVISUALIZING SUM ofVISUALIZING SUM of EEEEVVVVEEEENNNN NUMBERSNUMBERSNUMBERSNUMBERS
2
1
2 = 1 × 2
2 4 6 8
1 3 5 7
1 2 4 6
1 2 3 5
1 2 3 4
2 + 4 + 6 + 8 = 3 × 4
….
….
2 4 6 8 10 12 14 16
1 3 5 7 9 11 13 15
1 2 4 6 8 10 12 14
1 2 3 5 7 9 11 13
1 2 3 4 6 8 10 12
1 2 3 4 5 7 9 11
1 2 3 4 5 6 8 10
1 2 3 4 5 6 7 9
1 2 3 4 5 6 7 8
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 = 8 × 9 = 72
In general, 2 + 4 + 6 + 8 + … + (2n) = ݊ × ሺ݊ + 1ሻ
2 4
1 3
1 2
2 4 6
1 3 5
1 2 4
1 2 3
2 4 6 8 10
1 3 5 7 9
1 2 4 6 8
1 2 3 5 7
1 2 3 4 6
1 2 3 4 5
1 2 3 4 5
2 + 4 + 6 = 3 × 42 + 4 = 2 × 3
2 + 4 + 6 + 8 + 10 = 5 × 6 = 30

6. 27 । Power of ‘Visual Mathematics’ Copyright © 2018 by Vitthal B. Jadhav
1
From above figure, we can clearly visualize
3 fraction with size fits into fraction of .
Comparisons of Fractions
1)
From above diagram, we can clearly observe that
In general, in fractions having same denominator as the numerators
gets larger, the fraction becomes larger.
Example -

7. OTHER BOOKS