## Archives

#### A Mathematical Formulation to Design a House Pop-Up Card Using Paper Folding Technique

##### Abstract

Pop-up cards are folded papers from which three-dimensional structure appears when it is opened and can be folded afterwards. Constructing a pop-up card is relatively easy where anyone can just cut the pieces and attach them in the available template. Unfortunately, it is more difficult to design a pop-up card from scratch as they need to understand the pop-up cards mechanism and identify the position of the object correctly so popup cards do not overlap with each other. Therefore, this study provides an essential step and mathematical formula to help non-professional efficiently design and construct a simple house pop-up card that opens to 900. The main aspects discussed in the house pop-up card construction are the horizontal and vertical division, the width of the roof, the maximum length of the house and house's base, and the number of creases and planar faces. All mathematical equations were formulated based on the concepts of sequences, divisibility, and transformation ratio. It shows that the sequence, binary division, element of positive integer and geometry are related to each other. It is found that a beautiful design or proportion of house pop-up card can be created when 5  n where n is a positive integer.

Volume 11 | 12-Special Issue

Pages: 193-200