We extend the locus problems discussed in [9], [10] and [12], for a quadric surface when the fixed point is at an infinity. This paper will benefit those students who have backgrounds in Linear Algebra and Multivariable Calculus. As we shall see that the transformation from a quadric surface $\sum$ to its locus surface $\Delta$ is a linear transformation. Consequently, how the eigenvectors are related to the position of the fixed point at an infinity will be discussed.

We report on computing and visualizing the offsets of the Cassini ovals. We use the elimination technique to obtain offsets as envelopes of a family of planar curves in a recent experimental version of GeoGebra. Offset curves are obtained in their implicit form as irreducible polynomials of degree 12 and 16.

The cryptanalysis of the Enigma cipher machine during World War II by British and American codebreakers led by Alan Turing at Bletchley Park has been well-documented, and rightfully recognized as one of the supreme achievements of the human intellect. However, without the successful cryptanalysis of an earlier version of Enigma by Polish codebreakers led by Marian Rejewski in the 1930s, the work of the British and Americans in the 1940s might have taken much longer, prolonging the war at the potential cost of untold additional lives. The mathematics integral to the Polish cryptanalysis of Enigma involved some basic theory of permutations. The purpose of this paper is to present an overview of these ideas and how they served to this effect. To assist in demonstrating this, technology involving Maplets will be used.

Several researches show the potential of using new information and communication technologies (ICT) in the teaching and learning of mathematics. One of the branches in the teaching of mathematics that, over time, has deserved a special mention, is geometry, namely with the use of dynamic geometry systems (DGS). A learning environment for teaching and learning geometry, associated with tasks of an exploratory and investigative nature, tends to favor the discovery of properties and geometric relationships, which benefits the acquisition of knowledge and the production of evidence. In this article the learning environment Web Geometry Laboratory (WGL) was used in a case study for the exploration of visual proofs. The study was done with pre-service teachers. Conclusions are drawn and future work is foreseen.

In the first paper of this series, we discussed selected geometric concepts related to the class of patterns referred to as gereh. The creation of these patterns followed the rules of gereh (axioms). Constructions of such patterns follow three steps: construction of the contour for the pattern template, construction of tessellation inside the contour, and designing a pattern for each tessellation tile.
In this part, we will discuss why some patterns are considered incorrect and what are the fundamental features of a geometric pattern that make it acceptable?

Artificial Intelligence (AI) is one of the most crucial factor affecting future career choice of students. Accordingly, we offered students a semester-long Introductory Mathematics for Artificial Intelligence course. The course was developed to provide undergraduate students with various majors to navigate their career opportunities in AI-related jobs. This paper presents the newly published textbook and an online mathematics laboratory that integrated effective technology for this introductory course. In addition, we introduce a process-driven evaluation method based on the Problem/Project-Based Learning (PBL) report that worked well for this course. We also share trails of communications with our students and added the results of our students' performance analysis using principal component analyses (PCA) with the data generated from the class.