• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Math IA type I. Here is Lacsaps Fractions (the symmetrical pattern given) from n=1 until n=5, again with red numbers representing n:

Extracts from this document...

Introduction

Lacsap’s Fractions

A Math Internal Assessment

By Kelsey Kennelly

Lacsap’s Fractions…Ha

Clever, IB. You took the word “Pascal” and spelled it backwards to make “Lacsap”. I thought this was simply a Math Assessment but I guess it’s also a word scramble.

Anyways, with that being said, here is Pascal’s Triangle starting at n=0 until n=9, with red numbers representing n:

  1. 1
  2. 1        1
  3. 1        2        1
  4. 1        33        1
  5. 1        4        6        4        1
  6. 1        5        1010        5        1
  7. 1        6        15        20        15        6        1
  8. 1        7        21        35        35        21        7        1
  9. 1        8        28        46        70        46        28        8        1
  10. 1        9        36        84        126        126        84        36        9        1

*Column         0        1        2        3        4        5        6        7        8        9

*Columns rise diagonally from left to right. Column numbers will be represented by “c” followed by a subscript number.

Here is “Lacsap’s” Fractions (the symmetrical pattern given)

...read more.

Middle

The numbers of these numerators can be found in the above example of Pascal’s Triangle (column 2 or c2; or c7 but we’ll focus on c2). The number 1 can be found when n=2 in the second column (c2) of the triangle, which is the numerator of row 1 in Lacsap’s Fractions. Furthermore, when n=3 in the second column (c2) of Pascal’s Triangle, the number 3 is found, which is the numerator in Lacsap’s Fractions when n=2. This pattern continues, which brings me to the idea that the numerator is found by adding 1 to n in Lacsap’s fractions and finding that number in c2 of Pascal’s Triangle. For example, when n=3 in Lacsap’s Fractions, the numerator is 6. When you add 1 to 3, the result is 4; find n=4 in Pascal’s Triangle and find column 2.

...read more.

Conclusion

a =

a=   =

I used the quadratic equation to solve for row 2 and row 4. I used substitution to find the missing variables a and b to arrive at a general statement of

y = x2 + x

where y is the numerator and x is the row number (n)

I have already discovered that the numerator when n=6 is 21.

y = (6)2 + (6)

 y = (36)+ (6)

y = 18 + 3

y = 21

Now I will test the statement when n=7.

y = (7)2 + (7)

y = (49)+ (7)

y= 24.5 + 3.5

y = 28

This is correct because when n=7, 7+1=8. Find n=8 in Pascal’s Triangle in c2 and you will see the number 28. Now that I have discovered the general statement for the numerator, it is time to work on the denominator.

1        1

1                1

1                        1

1                                1

1                                        1

Column        1234        5

There is a pattern between the differences of numerator and denominator for each row. In row 1, for example,  is displayed and there is a difference of zero for numerator and denominator.  This continues in the symmetrical pattern.

Row

Column

Numerator – Denominator

1

1

0

2

1

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Extended Essay- Math

    �0�5�8�����z#b��0�3/4�-�Ji�ã°ï¿½"8J(tm)��� �r�A¸G[ñ5H�9"3�%[m�:(r)�å�4J'TF�cC���Â�>%�1-�'�*�� .1/2K�7<g���Â�0o~Ð���<��á¤ï¿½1/4�9t���| <HN� �B���mZH�� 3_Ah-k<e!�&-�#� +?=�0h=��An�"�i�1/4�>Mzau�?Ö¥r�'#'u'%�+ %è§ï¿½8���x��z�;�e&�hNHW×£- k�s�Q[�\�9����~��'{1/2���"�X'1/4Q�v�...-�1���Z"�V�MX-X�N8 -�;K:ԧ�>cIO'jD�����Ӧ'I'_�5(r)X�&��H;@6�1/4U-rdV"'�b��8e��VÆ~%�1/4��\`OxÒP_(G}L V ���%��,�KR�H'59��SV�K�<w>�(tm)~O����>bM$��`�źd*~'P"@�����(r)"�x���V3/4]�@o�;(r)��w�"{3 ""=�!�W�_���⦦lJz�����71ÿB� -�fÛ­g�JEV ���� �d` gRM/-jZ`^��Dc߸L ��"M�i��&"�5o�z�nqi|����K�J�-\�T"TV�%�B<��z/Ì(r)�"��=-� N71/2��pv}�E�pg˶�p(c)OB�Hd���L��xP���Kf[_-JM��q�1�O1/4��Oѱ�é§ï¿½ï¿½ï¿½c�A�)�-}�t3/4���5����6��t��o w��|+]*(tm)I,�-"�j��/��N��i""n���< �� O-@�x-]"�e�5o�}"��� t�"B�$ ϯ� b(c) $�C��ezU..._������fÒ�-r$Jg|�l�Je�PWJn1/4f6�𭨪"'�� .~q��"8��I(aE'G`C��\���(tm)��S��0��ccMG�����X~c��$��>9?�...o&�9p �� �-����>W���\�?*�8% ���KÄ°g3y-� ���0��>)�V���...��(r)Ss�'1/4L�'Y�v���� ](c)L.1/4s�XÆ��(tm)W3/4��\V�2h(c)�*%�>�È�9�(tm)W���:�| ��61/2��!+�R�h^�>J�$Y����-b�g�-�����B=0ZP� C=�,K�D�z�,�k�w�"� s�=1/2���� ��#N ��@:[}]�"�,�����"�`�C �"� ��o �'DC���!�C0 �1/48س�f�-��"~"V�'�LS��^(c)��-�C*�3/4��B�Ͽ��E�R�x������^�B�M,�]#6of'"��|x�Æ2c9�P}�;*�Y s����~��B>�k8T��?�Ð��0�C" (tm)n� ��� ��<bk"Ts8ï¿½ï¿½Þ ï¿½YF�-0�O���GxV�...y���-|1 <� 9�� +�[Nd �

  2. Math Studies I.A

    2209000000 6093.3636 Uzbekistan 2,600 64.98 168948 6760000 4222.4004 Venezuela 13,500 73.7 994950 182250000 5431.69 Virgin Islands 14,500 76.86 1114470 210250000 5907.4596 West Bank 2,900 73.46 213034 8410000 5396.3716 Yemen 2,400 62.5 150000 5760000 3906.25 Zimbabwe 200 39.5 7900 40000 1560.25 Total= 1707100 7914.39 130013258 51470030000 559261.8111 r = ,,??-????.-,,??-?? .??-??

  1. Math Studies - IA

    To do this, a potential model for correlation will be calculated, including relevant measures, such as the strength of that correlation. The question then arises whether, if a correlation becomes apparent, is indeed true. The Chi-squared test can be used to test if the two events are independent and if a potential dependency is due to chance.

  2. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

    The possibilities for losing for both the players Total number of possibilities 4 _ _ _ - = 1 = 1 2 2+8+20+40 = 70 5 _ _ _ _ - 4 4 8 6 _ _ _ _ _ - 10 10 20 7 _ _ _ _ _

  1. Math IA - Logan's Logo

    Thus, I determined the value of c=3.0. TO FIND d: As previously mentioned, changing the variable d will affect the vertical shift of the sine curve. If d>0 the graph is shifted vertically up; if d<0 then the graph is shifted vertically down. Thus adding or subtracting a constant to the sine function translates the graph parallel to the y-axis.

  2. Stellar Numbers. In this study, we analyze geometrical shapes, which lead to special numbers. ...

    4 61 As one can see, the numbers are identical, which supports the validity of the formula. Another example to prove the general statement as a stellar with 7 vertices (p=7) is going to be attempted below: n - Stage Number Tn as calculated manually , p=5 1 1 2

  1. MATH Lacsap's Fractions IA

    Therefore, the numerator of the sixth row will be 15 + 6 equaling to 21 (as stated before). This reinforces the correlation between Lacsap?s fractions and Pascal?s triangle. Also, there is a common 2nd difference of 1 in the numbers, which means that the numerators can be plugged into a quadratic formula.

  2. Gold Medal heights IB IA- score 15

    The slope of a quadratic function increases rapidly, causing this curve (figure 2) to not accurately represent the correlation of the data (figure 1). Cubic function- general equation f (x) = ax3 +bx2 +cx + d Figure 3 The simple cubic function of y= x3 must be modified in order to visualize the curvature of the function better.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work