Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas requires learning by self-discovery, they will be encouraged to see mathematical and real-world connections via mathematical demonstrations. They will have an opportunity to examine and construct their own meanings by recognising and demonstrating the same idea from different viewpoints with the help of technological tools. Such activities will help students to see that mathematics deals more importantly with ideas rather than formulas or algorithms, and that mathematical constructs are invented or created by human beings.